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

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12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 - Shaalaa.com
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Chapter 2: Integration

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 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)

Chapter 2: Integration

Q.1Q.2Q.3Q.4Q.5
12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 - Shaalaa.com

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.

Using SCERT Maharashtra Question Bank 12th Board Exam solutions Integration exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in SCERT Maharashtra Question Bank Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board 12th Board Exam prefer SCERT Maharashtra Question Bank Textbook Solutions to score more in exam.

Get the free view of chapter 2 Integration 12th Board Exam extra questions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 and can use Shaalaa.com to keep it handy for your exam preparation

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