SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 1.5 - Integration [Latest edition]

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SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 1.5 - Integration - Shaalaa.com
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Solutions for Chapter 1.5: Integration

Below listed, you can find solutions for Chapter 1.5 of Maharashtra State Board SCERT Maharashtra Question Bank for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022.


Q.1Q.2Q.3Q.4Q.5
Q.1

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 1.5 Integration Q.1

MCQ [1 Mark]

Q.1 | Q 1

Choose the correct alternative:

The value of `int ("d"x)/sqrt(1 - x)` is

  • `2sqrt(1 - x) + "c"`

  • `-2sqrt(1 - x) + "c"`

  • `sqrt(x) + "c"`

  • x + c

Q.1 | Q 2

Choose the correct alternative:

`int sqrt(1 + x)  "d"x` =

  • `x/2 sqrt(1 + x) + "c"`

  • `2/3(1 + x)^(3/2) + "c"`

  • `2/sqrt(1 + x) + "c"`

  • `(-3)/2 (1 + x) + "c"`

Q.1 | Q 3

Choose the correct alternative:

`intx^(2)3^(x^3) "d"x` =

  • `(3)^(x^3) + "c"`

  • `((3)^(x^3))/(3log3) + "c"`

  • `log 3*(3)^(x^3) + "c"`

  • `x^2 (3)^(x^2) + "c"`

Q.1 | Q 4

Choose the correct alternative:

`int (x + 2)/(2x^2 + 6x + 5) "d"x = "p"int (4x + 6)/(2x^2 + 6x + 5) "d"x + 1/2 int 1/(2x^2 + 6x + 5)"d"x`, then p = ?

  • `1/3`

  • `1/2`

  • `1/4`

  • 2

Q.1 | Q 5

`int ("d"x)/(x - x^2)` = ______

  • log x – log(1 – x) + c

  • log(1 – x2) + c

  • – log x + log(1 – x) + c

  • log(x – x2) + c

Q.1 | Q 6

Choose the correct alternative:

`int ("d"x)/((x - 8)(x + 7))` =

  • `1/15 log((x + 2)/(x - 1)) + "c"`

  • `1/15 log((x + 8)/(x + 7)) + "c"`

  • `1/15 log((x - 8)/(x + 7)) + "c"`

  • (x – 8)(x – 7) + c

Q.1 | Q 7

Choose the correct alternative:

`int(x + 1/x)^3 dx` = ______.

  • `1/4(x + 1/x)^4 + c`

  • `x^4/4 + (3x^2)/2 + 3log x - 1/(2x^2) + c`

  • `x^4/4 + (3x^2)/2 + 3log x + 1/x^2 + c`

  • `(x - x^(-1))^3 + c`

Q.1 | Q 8

Choose the correct alternative:

`int(("e"^(2x) + "e"^(-2x))/"e"^x) "d"x` =

  • `"e"^x - 1/(3"e"^(3x)) + "c"`

  • `"e"^x + 1/(3"e"^(3x)) + "c"`

  • `"e"^(-x) - 1/(3"e"^(3x)) + "c"`

  • `"e"^(-x) + 1/(3"e"^(3x)) + "c"`

Q.1 | Q 9

Choose the correct alternative:

`int(1 - x)^(-2) dx` = ______.

  • `(1 - x)^(-1) + c`

  • `(1 + x)^(-1) + c`

  • `(1 - x)^(-1) - 1 + c`

  • `(1 - x)^(-1) + 1 + c`

Q.1 | Q 10

Choose the correct alternative:

`int ((x^3 + 3x^2 + 3x + 1))/(x + 1)^5 "d"x` =

  • `(-1)/(x + 1) + "c"`

  • `((-1)/(x + 1))^5 + "c"`

  • log(x + 1) + c

  • 5log(x + 5) + c

Q.2

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 1.5 Integration Q.2

Fill in the blanks [1 Mark]

Q.2 | Q 1

`int 1/x  "d"x` = ______ + c

Q.2 | Q 2

`int 1/(x^2 - "a"^2)  "d"x` = ______ + c

Q.2 | Q 3

`int (7x + 9)^13  "d"x` ______ + c

Q.2 | Q 4

`int"e"^(4x - 3) "d"x` = ______ + c

Q.2 | Q 5

`int 5^(6x + 9) "d"x` = ______ + c

Q.2 | Q 6

`int (5(x^6 + 1))/(x^2 + 1) "d"x` = x5 – ______ x3 + 5x + c

Q.2 | Q 7

`int (x^2 + x - 6)/((x - 2)(x - 1))  "d"x` = x + ______ + c

Q.2 | Q 8

If f'(x) = `1/x + x` and f(1) = `5/2`, then f(x) = log x + `x^2/2` + ______ + c

Q.2 | Q 9

To find the value of `int ((1 + logx))/x` dx the proper substitution is ______

Q.2 | Q 10

`int 1/x^3 [log x^x]^2  "d"x` = p(log x)3 + c Then p = ______

Q.3

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 1.5 Integration Q.3

[1 Mark]

Q.3 | Q 1

State whether the following statement is True or False.

The proper substitution for `int x(x^x)^x (2log x + 1)  "d"x` is `(x^x)^x` = t

  • True

  • False

Q.3 | Q 2

State whether the following statement is True or False.

If `int x  "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.

  • True

  • False

Q.3 | Q 3

State whether the following statement is True or False:

If `int x  "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`

  • True

  • False

Q.3 | Q 4

State whether the following statement is True or False:

If `int((x - 1)"d"x)/((x + 1)(x - 2))` = A log|x + 1|  + B log|x – 2|, then A + B = 1

  • True

  • False

Q.3 | Q 5

State whether the following statement is True or False:

For `int (x - 1)/(x + 1)^3  "e"^x"d"x` = ex f(x) + c, f(x) = (x + 1)2

  • True

  • False

Q.3 | Q 6

State whether the following statement is True or False:

If f'(x) = 3x2 + 2x, then by definition of integration, we get f(x) = x3 + x2 + c 

  • True

  • False

Q.3 | Q 7

If f(x) = k, where k is constant, then `int "k"  "d"x` = 0

  • True

  • False

Q.3 | Q 8

State whether the following statement is True or False:

`int3^(2x + 3)  "d"x = (3^(2x + 3))/2 + "c"`

  • True

  • False

Q.3 | Q 9

State whether the following statement is True or False:

`int"e"^(4x - 7)  "d"x = ("e"^(4x - 7))/(-7) + "c"`

  • True

  • False

Q.3 | Q 10

State whether the following statement is True or False:

`int sqrt(1 + x^2) *x  "d"x = 1/3(1 + x^2)^(3/2) + "c"`

  • True

  • False

Q.4

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 1.5 Integration Q.4

Solve the following [3 Marks]

Q.4 | Q 1

Evaluate `int(3x^2 - 5)^2  "d"x`

Q.4 | Q 2

Evaluate `int 1/(x(x - 1))  "d"x`

Q.4 | Q 3

Evaluate `int 1/(x log x)  "d"x`

Q.4 | Q 4

Evaluate `int (2"e"^x + 5)/(2"e"^x + 1)  "d"x`

Q.4 | Q 5

Evaluate `int 1/(4x^2 - 1)  "d"x`

Q.4 | Q 6

Evaluate  `int"e"^x (1/x - 1/x^2)  "d"x`

Q.4 | Q 7

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

Q.4 | Q 8

Evaluate `int x log x  "d"x`

Q.4 | Q 9

Evaluate `int x^2"e"^(4x)  "d"x`

Q.4 | Q 10

Evaluate the following.

`int 1/(sqrt(3"x"^2 + 8))` dx

Q.5

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 1.5 Integration Q.5

Evaluate the following [4 Marks]

Q.5 | Q 1

`int "e"^x x/(x + 1)^2  "d"x`

Q.5 | Q 2

`int x^3"e"^(x^2) "d"x`

Q.5 | Q 3

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

Q.5 | Q 4

`int logx/(1 + logx)^2  "d"x`

Q.5 | Q 5

`int 1/sqrt(x^2 - 8x - 20)  "d"x`

Q.5 | Q 6

`int 1/(4x^2 - 20x + 17)  "d"x`

Q.5 | Q 7

`int (1 + x)/(x + "e"^(-x))  "d"x`

Q.5 | Q 8

Evaluate the following.

`int "x"^3/sqrt(1 + "x"^4)` dx

Q.5 | Q 9

`int (3"e"^(2"t") + 5)/(4"e"^(2"t") - 5)  "dt"`

Q.5 | Q 10

If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).

Solutions for Chapter 1.5: Integration

Q.1Q.2Q.3Q.4Q.5
SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 1.5 - Integration - Shaalaa.com

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 1.5 - Integration

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 1.5 Integration are Integration, Methods of Integration: Integration by Substitution, Methods of Integration: Integration by Parts, Methods of Integration: Integration Using Partial Fractions.

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Get the free view of Chapter 1.5, Integration 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 additional questions for Mathematics 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Maharashtra State Board, and you can use Shaalaa.com to keep it handy for your exam preparation.

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