# SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 2 - Integration [Latest edition]

## Chapter 2: Integration

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Q.1

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

Choose the correct alternative:

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 "d"x =

• 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) "d"x =

• (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 2 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 2 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

State whether the following statement is True or False:

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 2 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 int 1/sqrt(3x^2 + 8)  "d"x

Q.5

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

int x^3/sqrt(1 + x^4)  "d"x

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)

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## SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 2 - Integration

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 2 (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 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 2 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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