Maharashtra State BoardHSC Commerce 12th Board Exam
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Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board chapter 6 - Definite Integration [Latest edition]

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Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board - Shaalaa.com

Chapter 6: Definite Integration

Exercise 6.1Exercise 6.2Miscellaneous Exercise 6
Exercise 6.1 [Page 145]

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 6 Definite Integration Exercise 6.1 [Page 145]

Exercise 6.1 | Q 1 | Page 145

Evaluate the following definite integrals: `int_4^9 (1)/sqrt(x)*dx`

Exercise 6.1 | Q 2 | Page 145

Evaluate the following definite integrals: `int_(-2)^3 (1)/(x + 5)*dx`

Exercise 6.1 | Q 3 | Page 145

Evaluate the following definite integrals: `int_2^3 x/(x^2 - 1)*dx`

Exercise 6.1 | Q 4 | Page 145

Evaluate the following definite integrals: `int_0^1 (x^2 + 3x + 2)/sqrt(x)*dx`

Exercise 6.1 | Q 5 | Page 145

Evaluate the following definite integrals: `int_2^3 x/((x + 2)(x + 3))*dx`

Exercise 6.1 | Q 6 | Page 145

Evaluate the following definite integrals: `int_1^2 dx/(x^2 + 6x + 5)`

Exercise 6.1 | Q 7 | Page 145

Evaluate the following definite integrals: If `int_0^"a" (2x + 1)*dx` = 2, find the real value of a.

Exercise 6.1 | Q 8 | Page 145

Evaluate the following definite integrals: if `int_1^"a" (3x^2 + 2x + 1)*dx` = 11, find a.

Exercise 6.1 | Q 9 | Page 145

Evaluate the following definite integrals: `int_0^1 (1)/(sqrt(1 + x) + sqrt(x))*dx`

Exercise 6.1 | Q 10 | Page 145

Evaluate the following definite integrals: `int_1^2 (3x)/((9x^2 - 1))*dx`

Exercise 6.1 | Q 11 | Page 145

Evaluate the following definite integrals: `int_1^3 logx*dx`

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Exercise 6.2 [Page 148]

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 6 Definite Integration Exercise 6.2 [Page 148]

Exercise 6.2 | Q 1 | Page 148

Evaluate the following integrals : `int_(-9)^9 x^3/(4 - x^2)*dx`

Exercise 6.2 | Q 2 | Page 148

Evaluate the following integrals : `int_0^"a" x^2("a" - x)^(3/2)*dx`

Exercise 6.2 | Q 3 | Page 148

Evaluate the following integrals : `int_1^3 (root(3)(x + 5))/(root(3)(x + 5) + root(3)(9 - x))*dx`

Exercise 6.2 | Q 4 | Page 148

Evaluate the following integrals : `int_2^5 sqrt(x)/(sqrt(x) + sqrt(7 - x))*dx`

Exercise 6.2 | Q 5 | Page 148

Evaluate the following integrals : `int_1^2 sqrt(x)/(sqrt(3 - x) + sqrt(x))*dx`

Exercise 6.2 | Q 6 | Page 148

Evaluate the following integrals : `int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x))*dx`

Exercise 6.2 | Q 7 | Page 148

Evaluate the following integrals : `int_0^1 log(1/x - 1)*dx`

Exercise 6.2 | Q 8 | Page 148

Evaluate the following integrals : `int_0^1 x(1 - x)^5 *dx`

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Miscellaneous Exercise 6 [Pages 148 - 150]

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 6 Definite Integration Miscellaneous Exercise 6 [Pages 148 - 150]

Miscellaneous Exercise 6 | Q 1.01 | Page 148

Choose the correct alternative :

`int_(-9)^9 x^3/(4 - x^2)*dx` =

  • 0

  • 3

  • 9

  • – 9

Miscellaneous Exercise 6 | Q 1.02 | Page 148

Choose the correct alternative : 

`int_(-2)^3 dx/(x + 5)` =

  • `-log(8/3)`

  • `log(8/3)`

  • `log(3/8)`

  • `-log(3/8)`

Miscellaneous Exercise 6 | Q 1.03 | Page 148

Choose the correct alternative :

`int_2^3 x/(x^2 - 1)*dx` =

  • `log (8/3)`

  • `-log (8/3)`

  • `(1)/(2)log(8/3)`

  • `(-1)/(2)log(8/3)`

Miscellaneous Exercise 6 | Q 1.04 | Page 149

Choose the correct alternative : 

`int_4^9 dx/sqrt(x)` =

  • 9

  • 4

  • 2

  • 0

Miscellaneous Exercise 6 | Q 1.05 | Page 149

Choose the correct alternative :

If `int_0^"a" 3x^2*dx` = 8, then a = ?

  • 2

  • 0

  • `(8)/(3)`

  • a

Miscellaneous Exercise 6 | Q 1.06 | Page 149

Choose the correct alternative :

`int_2^3 x^4*dx` =

  • `(1)/(2)`

  • `(5)/(2)`

  • `(5)/(211)`

  • `(211)/(5)`

Miscellaneous Exercise 6 | Q 1.07 | Page 149

Choose the correct alternative :

`int_0^2 e^x*dx` =

  • e – 1

  • 1 – e

  • 1 – e2 

  • e2 – 1

Miscellaneous Exercise 6 | Q 1.08 | Page 149

Choose the correct alternative :

`int_"a"^"b" f(x)*dx` =

  • `int_"b"^"a" f(x)*dx`

  • `-int_"a"^"b" f(x)*dx`

  • `-int_"b"^"a" f(x)*dx`

  • `int_"0"^"a" f(x)*dx`

Miscellaneous Exercise 6 | Q 1.09 | Page 149

Choose the correct alternative :

`int_(-7)^7 x^3/(x^2 + 7)*dx` =

  • 7

  • 49

  • 0

  • `(7)/(2)`

Miscellaneous Exercise 6 | Q 1.1 | Page 149

Choose the correct alternative :

`int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x))*dx` =

  • `(7)/(2)`

  • `(5)/(2)`

  • 7

  • 2

Miscellaneous Exercise 6 | Q 2.01 | Page 149

Fill in the blank : `int_0^2 e^x*dx` = ________

Miscellaneous Exercise 6 | Q 2.02 | Page 149

Fill in the blank : `int_2^3 x^4*dx` = _______

Miscellaneous Exercise 6 | Q 2.03 | Page 149

Fill in the blank : `int_0^1 dx/(2x + 5)` = _______

Miscellaneous Exercise 6 | Q 2.04 | Page 149

Fill in the blank : If `int_0^"a" 3x^2*dx` = 8, then a = _______

Miscellaneous Exercise 6 | Q 2.05 | Page 149

Fill in the blank : `int_4^9 (1)/sqrt(x)*dx` = _______

Miscellaneous Exercise 6 | Q 2.06 | Page 149

Fill in the blank : `int_2^3 x/(x^2 - 1)*dx` = _______

Miscellaneous Exercise 6 | Q 2.07 | Page 149

Fill in the blank : `int_(-2)^3 dx/(x + 5)` = _______

Miscellaneous Exercise 6 | Q 2.08 | Page 149

Fill in the blank : `int_(-9)^9 x^3/(4 - x^2)*dx` = _______

Miscellaneous Exercise 6 | Q 3.01 | Page 149

State whether the following is True or False : `int_"a"^"b" f(x)*dx = int_(-"b")^(-"a") f(x)*dx`

  • True

  • False

Miscellaneous Exercise 6 | Q 3.02 | Page 149

State whether the following is True or False : `int_"a"^"b" f(x)*dx = int_"a"^"b" f("t")*dt`

  • True

  • False

Miscellaneous Exercise 6 | Q 3.03 | Page 149

State whether the following is True or False : `int_0^"a" f(x)*dx = int_"a"^0 f("a" - x)*dx`

  • True

  • False

Miscellaneous Exercise 6 | Q 3.04 | Page 149

State whether the following is True or False : `int_"a"^"b" f(x)*dx = int_"a"^"b" f(x - "a" - "b")*dx`

  • True

  • False

Miscellaneous Exercise 6 | Q 3.05 | Page 149

State whether the following is True or False : `int_(-5)^(5)  x^3/(x^2 + 7)*dx` = 0

  • True

  • False

Miscellaneous Exercise 6 | Q 3.06 | Page 150

State whether the following is True or False :  `int_1^2 sqrt(x)/(sqrt(3 - x) + sqrt(x))*dx = (1)/(2)`

  • True

  • False

Miscellaneous Exercise 6 | Q 3.07 | Page 150

State whether the following is True or False :  `int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x))*dx = (9)/(2)`

  • True

  • False

Miscellaneous Exercise 6 | Q 3.08 | Page 150

State whether the following is True or False : `int_4^7 ((11 - x)^2)/((11 - x)^2 + x^2)*dx = (3)/(2)`

  • True

  • False

Miscellaneous Exercise 6 | Q 4.01 | Page 150

Solve the following : `int_2^3 x/((x + 2)(x + 3))*dx`

Miscellaneous Exercise 6 | Q 4.02 | Page 150

Solve the following : `int_1^2 (x + 3)/(x (x + 2))*dx`

Miscellaneous Exercise 6 | Q 4.03 | Page 150

Solve the following : `int_1^3 x^2 log x*dx`

Miscellaneous Exercise 6 | Q 4.04 | Page 150

Solve the following : `int_0^1 e^(x^2)*x^3dx`

Miscellaneous Exercise 6 | Q 4.05 | Page 150

Solve the following : `int_1^2 e^(2x) (1/x - 1/(2x^2))*dx`

Miscellaneous Exercise 6 | Q 4.06 | Page 150

Solve the following : `int_4^9 (1)/sqrt(x)*dx`

Miscellaneous Exercise 6 | Q 4.07 | Page 150

Solve the following : `int_(-2)^3 (1)/(x + 5)*dx`

Miscellaneous Exercise 6 | Q 4.08 | Page 150

Solve the following : `int_2^3 x/(x^2 - 1)*dx`

Miscellaneous Exercise 6 | Q 4.09 | Page 150

Solve the following : `int_0^1 (x^2 + 3x + 2)/sqrt(x)*dx`

Miscellaneous Exercise 6 | Q 4.1 | Page 150

Solve the following : `int_3^5 dx/(sqrt(x + 4) + sqrt(x - 2)`

Miscellaneous Exercise 6 | Q 4.11 | Page 150

Solve the following : `int_2^3 x/(x^2 + 1)*dx`

Miscellaneous Exercise 6 | Q 4.12 | Page 150

Solve the following : `int_1^2 x^2*dx`

Miscellaneous Exercise 6 | Q 4.13 | Page 150

Solve the following : `int_(-4)^(-1) (1)/x*dx`

Miscellaneous Exercise 6 | Q 4.14 | Page 150

Solve the following : `int_0^1 (1)/(sqrt(1 + x) + sqrt(x))*dx`

Miscellaneous Exercise 6 | Q 4.15 | Page 150

Solve the following : `int_0^4 (1)/sqrt(x^2 + 2x + 3)*dx`

Miscellaneous Exercise 6 | Q 4.16 | Page 150

Solve the following : `int_2^4 x/(x^2 + 1)*dx`

Miscellaneous Exercise 6 | Q 4.17 | Page 150

Solve the following : `int_0^1 (1)/(2x - 3)*dx`

Miscellaneous Exercise 6 | Q 4.18 | Page 150

Solve the following : `int_1^2 (5x^2)/(x^2 + 4x + 3)*dx`

Miscellaneous Exercise 6 | Q 4.19 | Page 150

Solve the following : `int_1^2 dx/(x(1 + logx)^2`

Miscellaneous Exercise 6 | Q 4.2 | Page 150

Solve the following : `int_0^9 (1)/(1 + sqrt(x))*dx`

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Chapter 6: Definite Integration

Exercise 6.1Exercise 6.2Miscellaneous Exercise 6
Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board - Shaalaa.com

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board chapter 6 - Definite Integration

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board chapter 6 (Definite Integration) 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 Maharashtra State Board Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board chapter 6 Definite Integration are Fundamental Theorem of Integral Calculus, Properties of Definite Integrals.

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