Tamil Nadu Board of Secondary EducationHSC Commerce Class 12th
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Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Business Mathematics and Statistics Answers Guide chapter 2 - Integral Calculus – 1 [Latest edition]

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Class 12th Business Mathematics and Statistics Answers Guide - Shaalaa.com
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Chapter 2: Integral Calculus – 1

Exercise 2.1Exercise 2.2Exercise 2.3Exercise 2.4Exercise 2.5Exercise 2.6Exercise 2.7Exercise 2.8Exercise 2.9Exercise 2.10Exercise 2.11Exercise 2.12Miscellaneous problems
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Exercise 2.1 [Page 30]

Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Business Mathematics and Statistics Answers Guide Chapter 2 Integral Calculus – 1Exercise 2.1 [Page 30]

Exercise 2.1 | Q 1 | Page 30

Integrate the following with respect to x.

`sqrt(3x + 5)`

Exercise 2.1 | Q 2 | Page 30

Integrate the following with respect to x.

`(9x^2 - 4/x^2)^2`

Exercise 2.1 | Q 3 | Page 30

Integrate the following with respect to x.

(3 + x)(2 – 5x)

Exercise 2.1 | Q 4 | Page 30

Integrate the following with respect to x.

`sqrt(x)(x^3 - 2x + 3)`

Exercise 2.1 | Q 5 | Page 30

Integrate the following with respect to x.

`(8x + 13)/sqrt(4x + 7)`

Exercise 2.1 | Q 6 | Page 30

Integrate the following with respect to x.

`1/(sqrt(x + 1) + sqrt(x - 1))`

Exercise 2.1 | Q 7 | Page 30

Integrate the following with respect to x.

If f'(x) = x + b, f(1) = 5 and f(2) = 13, then find f(x)

Exercise 2.1 | Q 8 | Page 30

Integrate the following with respect to x.

If f'(x) = 8x3 – 2x and f(2) = 8, then find f(x)

Exercise 2.2 [Page 31]

Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Business Mathematics and Statistics Answers Guide Chapter 2 Integral Calculus – 1Exercise 2.2 [Page 31]

Exercise 2.2 | Q 1 | Page 31

Integrate the following with respect to x.

`(sqrt(2x) - 1/sqrt(2x))^2`

Exercise 2.2 | Q 2 | Page 31

Integrate the following with respect to x.

`(x^4 - x^2 + 2)/(x - 1)`

Exercise 2.2 | Q 3 | Page 31

Integrate the following with respect to x.

`x^3/(x + 2)`

Exercise 2.2 | Q 4 | Page 31

Integrate the following with respect to x.

`(x^3 + 3x^2 - 7x + 11)/(x + 5)`

Exercise 2.2 | Q 5 | Page 31

Integrate the following with respect to x.

`(3x + 2)/((x - 2)(x - 3))`

Exercise 2.2 | Q 6 | Page 31

Integrate the following with respect to x.

`(4x^2 + 2x + 6)/((x + 1)^2(x - 3))`

Exercise 2.2 | Q 7 | Page 31

Integrate the following with respect to x.

`(3x^2 - 2x + 5)/((x - 1)(x^2 + 5))`

Exercise 2.2 | Q 8 | Page 31

Integrate the following with respect to x.

If f'(x) = `1/x` and f(1) = `pi/4`, then find f(x)

Exercise 2.3 [Page 32]

Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Business Mathematics and Statistics Answers Guide Chapter 2 Integral Calculus – 1Exercise 2.3 [Page 32]

Exercise 2.3 | Q 1 | Page 32

Integrate the following with respect to x.

`"e"^(xlog"a") + "e"^("a"log"a") - "e"^("n"logx)`

Exercise 2.3 | Q 2 | Page 32

Integrate the following with respect to x.

`("a"^x - "e"^(xlog"b"))/("e"^(x log "a") "b"^x)`

Exercise 2.3 | Q 3 | Page 32

Integrate the following with respect to x.

`("e"^x + 1)^2 "e"^x`

Exercise 2.3 | Q 4 | Page 32

Integrate the following with respect to x.

`("e"^(3x) - "e"^(-3x))/"e"^x`

Exercise 2.3 | Q 5 | Page 32

Integrate the following with respect to x.

`("e"^(3x) +"e"^(5x))/("e"^x + "e"^-x)`

Exercise 2.3 | Q 6 | Page 32

Integrate the following with respect to x.

`[1 - 1/2]"e"^((x + 1/x))`

Exercise 2.3 | Q 7 | Page 32

Integrate the following with respect to x.

`1/(x(log x)^2`

Exercise 2.3 | Q 8 | Page 32

Integrate the following with respect to x.

If f'(x) = ex and f(0) = 2, then find f(x)

Exercise 2.4 [Page 33]

Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Business Mathematics and Statistics Answers Guide Chapter 2 Integral Calculus – 1Exercise 2.4 [Page 33]

Exercise 2.4 | Q 1 | Page 33

Integrate the following with respect to x.

2 cos x – 3 sin x + 4 sec2x – 5 cosec2x

Exercise 2.4 | Q 2 | Page 33

Integrate the following with respect to x.

sin3x

Exercise 2.4 | Q 3 | Page 33

Integrate the following with respect to x.

`(cos 2x + 2sin^2x)/(cos^2x)`

Exercise 2.4 | Q 4 | Page 33

Integrate the following with respect to x.

`1/(sin^2x cos^2x) ["Hint:" sin^2x + cos^2x = 1]`

Exercise 2.4 | Q 5 | Page 33

Integrate the following with respect to x.

`sqrt(1 - sin 2x)`

Exercise 2.5 [Page 35]

Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Business Mathematics and Statistics Answers Guide Chapter 2 Integral Calculus – 1Exercise 2.5 [Page 35]

Exercise 2.5 | Q 1 | Page 35

Integrate the following with respect to x.

xe–x 

Exercise 2.5 | Q 2 | Page 35

Integrate the following with respect to x.

x3e3x

Exercise 2.5 | Q 3 | Page 35

Integrate the following with respect to x.

log x

Exercise 2.5 | Q 4 | Page 35

Integrate the following with respect to x.

x log x

Exercise 2.5 | Q 5 | Page 35

Integrate the following with respect to x.

xn log x

Exercise 2.5 | Q 6 | Page 35

Integrate the following with respect to x.

`x^5  "e"^x`

Exercise 2.6 [Page 38]

Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Business Mathematics and Statistics Answers Guide Chapter 2 Integral Calculus – 1Exercise 2.6 [Page 38]

Exercise 2.6 | Q 1 | Page 38

Integrate the following with respect to x.

`(2x + 5)/(x^2 + 5x - 7)`

Exercise 2.6 | Q 2 | Page 38

Integrate the following with respect to x.

`("e"^(3logx))/(x^4 + 1)`

Exercise 2.6 | Q 3 | Page 38

Integrate the following with respect to x.

`"e"^(2x)/("e"^(2x) - 2)`

Exercise 2.6 | Q 4 | Page 38

Integrate the following with respect to x.

`(log x)^3/x`

Exercise 2.6 | Q 5 | Page 38

Integrate the following with respect to x.

`(6x + 7)/sqrt(3x^2 + 7x - 1)`

Exercise 2.6 | Q 6 | Page 38

Integrate the following with respect to x.

`(4x + 2) sqrt(x^2 + x + 1)`

Exercise 2.6 | Q 7 | Page 38

Integrate the following with respect to x.

x8(1 + x9)5 

Exercise 2.6 | Q 8 | Page 38

Integrate the following with respect to x.

`(x^("e" - 1) + "e"^(x - 1))/(x^"e" + "e"^x)`

Exercise 2.6 | Q 9 | Page 38

Integrate the following with respect to x

`1/(x log x)`

Exercise 2.6 | Q 10 | Page 38

Integrate the following with respect to x.

`x/(2x^4 - 3x^2 - 2)`

Exercise 2.6 | Q 11 | Page 38

Integrate the following with respect to x.

ex(1 + x) log(xex)

Exercise 2.6 | Q 12 | Page 38

Integrate the following with respect to x.

`1/(x^2(x^2 + 1))`

Exercise 2.6 | Q 13 | Page 38

Integrate the following with respect to x.

`"e"^x [1/x^2 - 2/x^3]`

Exercise 2.6 | Q 14 | Page 38

Integrate the following with respect to x.

`"e"^x [(x - 1)/(x + 1)^3]`

Exercise 2.6 | Q 15 | Page 38

Integrate the following with respect to x.

`"e"^(3x) [(3x - 1)/(9x^2)]`

Exercise 2.7 [Page 42]

Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Business Mathematics and Statistics Answers Guide Chapter 2 Integral Calculus – 1Exercise 2.7 [Page 42]

Exercise 2.7 | Q 1 | Page 42

Integrate the following with respect to x.

`1/(9 - 16x^2)`

Exercise 2.7 | Q 2 | Page 42

Integrate the following with respect to x.

`1/(9 - 8x - x^2)`

Exercise 2.7 | Q 3 | Page 42

Integrate the following with respect to x.

`1/(2x^2 - 9)`

Exercise 2.7 | Q 4 | Page 42

Integrate the following with respect to x.

`1/(x^2 - x - 2)`

Exercise 2.7 | Q 5 | Page 42

Integrate the following with respect to x.

`1/(x^2 + 3x + 2)`

Exercise 2.7 | Q 6 | Page 42

Integrate the following with respect to x.

`1/(2x^2 + 6x - 8)`

Exercise 2.7 | Q 7 | Page 42

Integrate the following with respect to x.

`"e"^x/("e"^(2x) - 9)`

Exercise 2.7 | Q 8 | Page 42

Integrate the following with respect to x.

`1/sqrt(9x^2 - 7)`

Exercise 2.7 | Q 9 | Page 42

Integrate the following with respect to x.

`1/sqrt(x^2 + 6x + 13)`

Exercise 2.7 | Q 10 | Page 42

Integrate the following with respect to x.

`1/sqrt(x^2 - 3x + 2)`

Exercise 2.7 | Q 11 | Page 42

Integrate the following with respect to x.

`x^3/sqrt(x^8 - 1)`

Exercise 2.7 | Q 12 | Page 42

Integrate the following with respect to x.

`sqrt(1 + x + x^2)`

Exercise 2.7 | Q 13 | Page 42

Integrate the following with respect to x.

`sqrt(x^2 - 2)`

Exercise 2.7 | Q 14 | Page 42

Integrate the following with respect to x.

`sqrt(4x^2 - 5)`

Exercise 2.7 | Q 15 | Page 42

Integrate the following with respect to x.

`sqrt(2x^2 + 4x + 1)`

Exercise 2.7 | Q 16 | Page 42

Integrate the following with respect to x.

`1/(x + sqrt(x^2 - 1)`

Exercise 2.8 [Page 47]

Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Business Mathematics and Statistics Answers Guide Chapter 2 Integral Calculus – 1Exercise 2.8 [Page 47]

Exercise 2.8 | Q I.1 | Page 47

Using second fundamental theorem, evaluate the following:

`int_0^1 "e"^(2x)  "d"x`

Exercise 2.8 | Q I.2 | Page 47

Using second fundamental theorem, evaluate the following:

`int_0^(1/4) sqrt(1 - 4)  "d"x`

Exercise 2.8 | Q I.3 | Page 47

Using second fundamental theorem, evaluate the following:

`int_1^2 (x "d"x)/(x^2 + 1)`

Exercise 2.8 | Q I.4 | Page 47

Using second fundamental theorem, evaluate the following:

`int_0^3 ("e"^x "d"x)/(1 + "e"^x)`

Exercise 2.8 | Q I.5 | Page 47

Using second fundamental theorem, evaluate the following:

`int_0^1 x"e"^(x^2)  "d"x`

Exercise 2.8 | Q I.6 | Page 47

Using second fundamental theorem, evaluate the following:

`int_1^"e" ("d"x)/(x(1 + logx)^3`

Exercise 2.8 | Q I.7 | Page 47

Using second fundamental theorem, evaluate the following:

`int_(-1)^1 (2x + 3)/(x^2 + 3x + 7)  "d"x`

Exercise 2.8 | Q I.8 | Page 47

Using second fundamental theorem, evaluate the following:

`int_0^(pi/2) sqrt(1 + cos x)  "d"x`

Exercise 2.8 | Q I.9 | Page 47

Using second fundamental theorem, evaluate the following:

`int_1^2 (x - 1)/x^2  "d"x`

Exercise 2.8 | Q II. 1 | Page 47

Evaluate the following:

`int_1^4` f(x) dx where f(x) = `{{:(4x + 3",", 1 ≤ x ≤ 2),(3x + 5",", 2 < x ≤ 4):}`

Exercise 2.8 | Q II.2 | Page 47

Evaluate the following:

`int_0^2 "f"(x)  "d"x` where f(x) = `{{:(3 - 2x - x^2",", x ≤ 1),(x^2 + 2x - 3",", 1 < x ≤ 2):}`

Exercise 2.8 | Q II.3 | Page 47

Evaluate the following:

`int_(-1)^1 "f"(x)  "d"x` where f(x) = `{{:(x",", x ≥ 0),(-x",", x  < 0):}`

Exercise 2.8 | Q II.4 | Page 47

Evaluate the following:

f(x) = `{{:("c"x",", 0 < x < 1),(0",",  "otherwise"):}` Find 'c" if `int_0^1 "f"(x)  "d"x` = 2

Exercise 2.9 [Page 50]

Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Business Mathematics and Statistics Answers Guide Chapter 2 Integral Calculus – 1Exercise 2.9 [Page 50]

Exercise 2.9 | Q 1 | Page 50

Evaluate the following using properties of definite integral:

`int_(- pi/4)^(pi/4) x^3 cos^3 x  "d"x`

Exercise 2.9 | Q 2 | Page 50

Evaluate the following using properties of definite integral:

`int_(- pi/2)^(pi/2) sin^2theta  "d"theta`

Exercise 2.9 | Q 3 | Page 50

Evaluate the following using properties of definite integral:

`int_(-1)^1 log ((2 - x)/(2 + x))  "d"x`

Exercise 2.9 | Q 4 | Page 50

Evaluate the following using properties of definite integral:

`int_0^(i/2) (sin^7x)/(sin^7x + cos^7x)  "d"x`

Exercise 2.9 | Q 5 | Page 50

Evaluate the following using properties of definite integral:

`int_0^1 log (1/x - 1)  "d"x`

Exercise 2.9 | Q 6 | Page 50

Evaluate the following using properties of definite integral:

`int_0^1 x/((1 - x)^(3/4))  "d"x`

Exercise 2.10 [Page 51]

Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Business Mathematics and Statistics Answers Guide Chapter 2 Integral Calculus – 1Exercise 2.10 [Page 51]

Exercise 2.10 | Q 1 | Page 51

Evaluate the following:

Γ(4)

Exercise 2.10 | Q 1. (ii) | Page 51

Evaluate the following:

`Γ (9/2)`

Exercise 2.10 | Q 1. (iii) | Page 51

Evaluate the following:

`int_0^oo "e"^(-mx) x^6 "d"x`

Exercise 2.10 | Q 1. (iv) | Page 51

Evaluate the following:

`int_0^oo "e"^(-4x) x^4  "d"x`

Exercise 2.10 | Q 1. (v) | Page 51

Evaluate the following:

`int_0^oo "e"^(- x/2) x^5  "d"x`

Exercise 2.10 | Q 2 | Page 51

If f(x) = `{{:(x^2"e"^(-2x)",", x ≥ 0),(0",", "otherwise"):}`, then evaluate `int_0^oo "f"(x) "d"x`

Exercise 2.11 [Page 53]

Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Business Mathematics and Statistics Answers Guide Chapter 2 Integral Calculus – 1Exercise 2.11 [Page 53]

Exercise 2.11 | Q 1 | Page 53

Evaluate the following integrals as the limit of the sum:

`int_0^1 (x + 4)  "d"x`

Exercise 2.11 | Q 2 | Page 53

Evaluate the following integrals as the limit of the sum:

`int_1^3 x  "d"x`

Exercise 2.11 | Q 3 | Page 53

Evaluate the following integrals as the limit of the sum:

`int_1^3 (2x + 3)  "d"x`

Exercise 2.11 | Q 4 | Page 53

Evaluate the following integrals as the limit of the sum:

`int_0^1 x^2  "d"x`

Exercise 2.12 [Pages 53 - 55]

Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Business Mathematics and Statistics Answers Guide Chapter 2 Integral Calculus – 1Exercise 2.12 [Pages 53 - 55]

MCQ

Exercise 2.12 | Q 1 | Page 53

Choose the correct alternative:

`int 1/x^3  "d"x` is

  • `(-3)/(x^2) + "c"`

  • `(-1)/(2x^2) + "c"`

  • `(-1)/(3x^2) + "c"`

  • `(-2)/(x^2) + "c"`

Exercise 2.12 | Q 2 | Page 53

Choose the correct alternative:

`int 2^x  "d"x` is

  • 2x log 2 + c

  • 2x + c

  • `2^x/log2 + "c"`

  • `log2/2^x + "c"`

Exercise 2.12 | Q 3 | Page 53

Choose the correct alternative:

`int (sin2x)/(2sinx)  "d"x` is

  • sin x + c

  • `1/2 sin x + "c"`

  • `cos x + "c"`

  • `1/2 cos x + "c"`

Exercise 2.12 | Q 4 | Page 53

Choose the correct alternative:

`int (sin5x - sinx)/(cos3x)  "d"x` is

  • − cos 2x + c

  • − cos 2x + c

  • `- 1/4 cos 2x + "c"`

  • − 4 cos 2x + c

Exercise 2.12 | Q 5 | Page 53

Choose the correct alternative:

`int logx/x  "d"x, x > 0` is

  • `1/2 (log x)^2 + "c"`

  • `- 1/2 (log x)^2`

  • `2/x^2 + "c"`

  • `2/x^2 - "c"`

Exercise 2.12 | Q 6 | Page 53

Choose the correct alternative:

`int "e"^x/sqrt(1 + "e"^x)  "d"x` is

  • `"e"^x/sqrt(1 + "e"^x) + "c"`

  • `2sqrt(1 + "e"^x) + "c"`

  • `sqrt(1 + "e"^x) + "c"`

  • `"e"^x sqrt(1 + "e"^x) + "c"`

Exercise 2.12 | Q 7 | Page 53

Choose the correct alternative:

`int sqrt("e"^x) "d"x` is

  • `sqrt("e"^x) + "c"`

  • `2sqrt("e"^x) + "c"`

  • `1/2 sqrt("e"^x) + "c"`

  • `1/(2sqrt("e"^x)) + "c"`

Exercise 2.12 | Q 8 | Page 53

Choose the correct alternative:

`int "e"^(2x) [2x^2 + 2x]  "d"x`

  • `"e"^(2x)x^2 + "c"`

  • `x"e"^(2x) + "c"`

  • `2x^2"e"^2 + "c"`

  • `(x^2"e"^x)/2 + "c"`

Exercise 2.12 | Q 9 | Page 53

Choose the correct alternative:

`int "e"^x/("e"^x + 1)  "d"x` is

  • `log|"e"^x/("e"^x + 1)| + "c"`

  • `log|("e"^x + 1)/"e"| + "c"`

  • `log|"e"^x| + "c"`

  • `log|"e"^x + 1| + "c"`

Exercise 2.12 | Q 10 | Page 53

Choose the correct alternative:

`int[9/(x - 3) - 1/(x + 1)]  "d"x` is

  • `log |x - 3| - log |x + 1| + "c"`

  • `log |x - 3| + log |x + 1| + "c"`

  • `9log |x - 3| - log |x + 1| + "c"`

  • `9log |x - 3| + log |x + 1| + "c"`

Exercise 2.12 | Q 11 | Page 53

Choose the correct alternative:

`int (2x^3)/(4 + x^4)  "d"x` is

  • `log |4 + x^4| + "c"`

  • `1/2 log |4 + x^4| + "c"`

  • `1/4 log |4 + x^4| + "c"`

  • `log |2x^3/(4 + x^4) + "c"`

Exercise 2.12 | Q 12 | Page 53

Choose the correct alternative:

`int ("d"x)/sqrt(x^2 - 36) + "c"`

  • `sqrt(x^2 - 36) + "c"`

  • `log |x + sqrt(x^2 - 36)| + "c"`

  • `log |x - sqrt(x^2 - 36)| + "c"`

  • `log |x^2 + sqrt(x^2 - 36)| + "c"`

Exercise 2.12 | Q 13 | Page 54

Choose the correct alternative:

`int (2x + 3)/sqrt(x^2 + 3x + 2)  "d"x` is

  • `sqrt(x^2 + 3x + 2) + "c"`

  • `2sqrt(x^2 + 3x + 2) + "c"`

  • `log(x^2 + 3x + 2) + "c"`

  • `2/3(x^2 + 3x + 2) + "c"`

Exercise 2.12 | Q 14 | Page 54

Choose the correct alternative:

`int_0^1 (2x + 1)  "d"x` is

  • 1

  • 2

  • 3

  • 4

Exercise 2.12 | Q 15 | Page 54

Choose the correct alternative:

`int_2^4 ("d"x)/x` is

  • log 4

  • 0

  • log 2

  • log 8

Exercise 2.12 | Q 16 | Page 54

Choose the correct alternative:

`int_0^oo "e"^(-2x)  "d"x` is

  • 0

  • 1

  • 2

  • `1/2`

Exercise 2.12 | Q 17 | Page 54

Choose the correct alternative:

`int_(-1)^1 x^3 "e"^(x^4)  "d"x` is

  • 1

  • `2 int_0^1 x^3  "e"^(x^4)  "d"x`

  • 0

  • `"e"^(x^4)`

Exercise 2.12 | Q 18 | Page 54

Choose the correct alternative:

If f(x) is a continuous function and a < c < b, then `int_"a"^"c" f(x)  "d"x + int_"c"^"b" f(x)  "d"x` is

  • `int_"a"^"b" f(x)  "d"x - int_"a"^"c" f(x)  "d"x`

  • `int_"a"^"c" f(x)  "d"x - int_"a"^"b" f(x)  "d"x`

  • `int_"a"^"b" f(x)  "d"x`

  • 0

Exercise 2.12 | Q 19 | Page 54

Choose the correct alternative:

The value of `int_(- pi/2)^(pi/2) cos  x  "d"x` is

  • 0

  • 2

  • 1

  • 4

Exercise 2.12 | Q 20 | Page 54

Choose the correct alternative:

`int_0^1 sqrt(x^4 (1 - x)^2)  "d"x` is

  • `1/12`

  • `(-7)/12`

  • `7/12`

  • `(-1)/12`

Exercise 2.12 | Q 21 | Page 54

Choose the correct alternative:

If `int_0^1 f(x)  "d"x = 1, int_0^1 x  f(x)  "d"x = "a"`, and `int_0^1 x^2 f(x)  "d"x = "a"^2`, then `int_0^1 ("a" - x)^2 f(x)  "d"x` is

  • 4a2

  • 0

  • 2a2

  • 1

Exercise 2.12 | Q 22 | Page 54

Choose the correct alternative:

The value of `int_2^3 f(5 - 3)  "d"x - int_2^3 f(x)  "d"x` is

  • 1

  • 0

  • – 1

  • 5

Exercise 2.12 | Q 23 | Page 54

Choose the correct alternative:

`int_0^4 (sqrt(x) + 1/sqrt(x))  "d"x` is

  • `20/3`

  • `21/3`

  • `28/3`

  • `1/3`

Exercise 2.12 | Q 24 | Page 54

Choose the correct alternative:

`int_0^(pi/3) tan x  "d"x` is

  • log 2

  • 0

  • `log sqrt(2)`

  • 2 log 2

Exercise 2.12 | Q 25 | Page 54

Choose the correct alternative:

Using the factorial representation of the gamma function, which of the following is the solution for the gamma function Γ(n) when n = 8 is

  • 5040

  • 5400

  • 4500

  • 5540

Exercise 2.12 | Q 26 | Page 54

Choose the correct alternative:

Γ(n) is

  • (n – 1)!

  • n!

  • n Γ(n)

  • (n – 1) Γ(n)

Exercise 2.12 | Q 27 | Page 54

Choose the correct alternative:

Γ(1) is

  • 0

  • 1

  • n

  • n!

Exercise 2.12 | Q 28 | Page 54

Choose the correct alternative:

If n > 0, then Γ(n) is

  • `int_0^1 "e"^-x x^("n" - 1) "d"x`

  • `int_0^1 "e"^-x x^"n" "d"x`

  • `int_0^oo "e"^x x^-"n" "d"x`

  • `int_0^oo "e"^-x x^("n" - 1) "d"x`

Exercise 2.12 | Q 29 | Page 55

Choose the correct alternative:

`Γ(3/2)`

  • `sqrt(pi)`

  • `sqrt(pi)/2`

  • `2sqrt(pi)`

  • `3/2`

Exercise 2.12 | Q 30 | Page 55

Choose the correct alternative:

`int_0^oo x^4"e"^-x  "d"x` is

  • 12

  • 4

  • 4!

  • 64

Miscellaneous problems [Page 55]

Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Business Mathematics and Statistics Answers Guide Chapter 2 Integral Calculus – 1Miscellaneous problems [Page 55]

Miscellaneous problems | Q 1 | Page 55

Evaluate the following integral:

`int 1/(sqrt(x + 2) - sqrt(x + 3))  "d"x`

Miscellaneous problems | Q 2 | Page 55

Evaluate the following integral:

`int ("d"x)/(2 - 3x - 2x^2)`

Miscellaneous problems | Q 3 | Page 55

Evaluate the following integral:

`int ("d"x)/("e"^x + 6 + 5"e"^-x)`

Miscellaneous problems | Q 4 | Page 55

Evaluate the following integral:

`int sqrt(2x^2 - 3)  "d"x`

Miscellaneous problems | Q 5 | Page 55

Evaluate the following integral:

`sqrt(9x^2 + 12x + 3)  "d"x`

Miscellaneous problems | Q 6 | Page 55

Evaluate the following integral:

`int (x + 1)^2 log x  "d"x`

Miscellaneous problems | Q 7 | Page 55

Evaluate the following integral:

`int log (x - sqrt(x^2 - 1)) "d"x`

Miscellaneous problems | Q 8 | Page 55

Evaluate the following integral:

`int_0^1 sqrt(x(x - 1))  "d"x`

Miscellaneous problems | Q 9 | Page 55

Evaluate the following integral:

`int_(-1)^1 x^2 "e"^(-2x)  "d"x`

Miscellaneous problems | Q 10 | Page 55

Evaluate the following integral:

`int_0^3 (x dx)/(sqrt(x + 1)+ sqrt(5x + 1))`

Chapter 2: Integral Calculus – 1

Exercise 2.1Exercise 2.2Exercise 2.3Exercise 2.4Exercise 2.5Exercise 2.6Exercise 2.7Exercise 2.8Exercise 2.9Exercise 2.10Exercise 2.11Exercise 2.12Miscellaneous problems
Class 12th Business Mathematics and Statistics Answers Guide - Shaalaa.com

Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Business Mathematics and Statistics Answers Guide chapter 2 - Integral Calculus – 1

Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Business Mathematics and Statistics Answers Guide chapter 2 (Integral Calculus – 1) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Tamil Nadu Board of Secondary Education Class 12th Business Mathematics and Statistics Answers Guide solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 12th Business Mathematics and Statistics Answers Guide chapter 2 Integral Calculus – 1 are Indefinite Integrals, Definite Integrals.

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