#### Online Mock Tests

#### Chapters

Chapter 1.2: Matrices

Chapter 1.3: Differentiation

Chapter 1.4: Applications of Derivatives

▶ Chapter 1.5: Integration

Chapter 1.6: Definite Integration

Chapter 1.7: Application of Definite Integration

Chapter 1.8: Differential Equation and Applications

Chapter 2.1: Commission, Brokerage and Discount

Chapter 2.2: Insurance and Annuity

Chapter 2.3: Linear Regression

Chapter 2.4: Time Series

Chapter 2.5: Index Numbers

Chapter 2.6: Linear Programming

Chapter 2.7: Assignment Problem and Sequencing

Chapter 2.8: Probability Distributions

###### Advertisements

###### Advertisements

## 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.

### 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]

**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

**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"`

**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"`

**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

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

log x – log(1 – x) + c

log(1 – x

^{2}) + c– log x + log(1 – x) + c

log(x – x

^{2}) + c

**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

**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`

**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"`

**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`

**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

### 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]

`int 1/x "d"x` = ______ + c

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

`int (7x + 9)^13 "d"x` ______ + c

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

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

`int (5(x^6 + 1))/(x^2 + 1) "d"x` = x^{5} – ______ x^{3} + 5x + c

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

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

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

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

### 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]

**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

**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

**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

**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

**State whether the following statement is True or False:**

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

True

False

**State whether the following statement is True or False:**

If f'(x) = 3x^{2} + 2x, then by definition of integration, we get f(x) = x^{3} + x^{2} + c

True

False

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

True

False

**State whether the following statement is True or False:**

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

True

False

**State whether the following statement is True or False:**

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

True

False

**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

### 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]

Evaluate `int(3x^2 - 5)^2 "d"x`

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

Evaluate `int 1/(x log x) "d"x`

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

Evaluate `int 1/(4x^2 - 1) "d"x`

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

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

Evaluate `int x log x "d"x`

Evaluate `int x^2"e"^(4x) "d"x`

**Evaluate the following.**

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

### 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]

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

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

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

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

`int 1/sqrt(x^2 - 8x - 20) "d"x`

`int 1/(4x^2 - 20x + 17) "d"x`

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

**Evaluate the following.**

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

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

If f '(x) = 4x^{3} - 3x^{2} + 2x + k, f(0) = 1 and f(1) = 4, find f(x).

## Solutions for Chapter 1.5: Integration

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

Shaalaa.com has the Maharashtra State Board Mathematics 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. SCERT Maharashtra Question Bank solutions for Mathematics 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Maharashtra State Board 1.5 (Integration) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. SCERT Maharashtra Question Bank textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.

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.

Using SCERT Maharashtra Question Bank 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 solutions Integration exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in SCERT Maharashtra Question Bank Solutions are essential questions that can be asked in the final exam. Maximum Maharashtra State Board 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 students prefer SCERT Maharashtra Question Bank Textbook Solutions to score more in exams.

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.