SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 1.6 - Definite 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 1.6 - Definite Integration - Shaalaa.com
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Solutions for Chapter 1.6: Definite Integration

Below listed, you can find solutions for Chapter 1.6 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.5Q.6
Q.1

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 1.6 Definite Integration Q.1

MCQ [1 Mark]

Q.1 | Q 1

Choose the correct alternative:

`int_2^3 x^4  "d"x` =

  • `1/2`

  • `5/2`

  • `5/211`

  • `211/5`

Q.1 | Q 2

Choose the correct alternative:

`int_0^"a" 3x^5  "d"x` = 8, then a =

  • 2

  • 0

  • `8/3`

  • a

Q.1 | Q 3

Choose the correct alternative:

`int_4^9 ("d"x)/sqrt(x)` =

  • 9

  • 4

  • 2

  • 0

Q.1 | Q 4

`int_0^2 e^x dx` = ______.

  • e2 – 1

  • 1 – e2 

  • e – 1

  • 1 – e

Q.1 | Q 5

Choose the correct alternative:

`int_(-2)^3 1/(x + 5)  "d"x` =

  • `log (3/8)`

  • `log (8/3)`

  • `log (8/5)`

  • 0

Q.1 | Q 6

Choose the correct alternative:

`int_2^3 x/(x^2 - 1)  "d"x` =

  • `log (8/3)`

  • `- log (8/3)`

  • `1/2 log(8/3)`

  • `-1/2 log(8/3)`

Q.1 | Q 7

`int_"a"^"b" "f"(x)  "d"x` = ______

  • `int_"b"^"a" "f"(x)  "d"x`

  • `- int_"a"^"b" "f"(x)  "d"x`

  • `- int_"b"^"a" "f"(x)  "d"x`

  • `int_0^"a" "f"(x)  "d"x`

Q.1 | Q 8

`int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x))  "d"x` = ______

  • `7/2`

  • `5/2`

  • 7

  • 2

Q.1 | Q 9

Choose the correct alternative:

`int_(-9)^9 x^3/(4 - x^2)  "d"x` =

  • 0

  • 3

  • 9

  • – 9

Q.2

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 1.6 Definite Integration Q.2

Fill in the blanks [1 Mark]

Q.2 | Q 1

`int_1^2 x^2  "d"x` = ______

Q.2 | Q 2

`int_0^"a" 4x^3  "d"x` = 81, then a = ______

Q.2 | Q 3

`int_0^1 "e"^(2x) "d"x` = ______

Q.2 | Q 4

`int_1^2 1/(2x + 3)  dx` = ______

Q.2 | Q 5

`int_2^4 x/(x^2 + 1)  "d"x` = ______

Q.2 | Q 6

`int_(-7)^7 x^3/(x^2 + 7)  "d"x` = ______

Q.3

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 1.6 Definite Integration Q.3

[1 Mark]

Q.3 | Q 1

State whether the following statement is True or False:

`int_0^"a" 3x^2  "d"x` = 27, then a = 2.5

  • True

  • False

Q.3 | Q 2

State whether the following statement is True or False:

`int_0^1 1/(2x + 5)  "d"x = log(7/5)`

  • True

  • False

Q.3 | Q 3

State whether the following statement is True or False: 

`int_2^3 x/(x^2 + 1)  "d"x = 1/2 log 2`

  • True

  • False

Q.3 | Q 4

State whether the following statement is True or False:

`int_"a"^"b" "f"(x)  "d"x = int_"a"^"b" "f"("a" + "b" - x)  "d"x`

  • True

  • False

Q.3 | Q 5

State whether the following statement is True or False: 

`int_0^(2"a") "f"(x)  "d"x = int_0^"a" "f"(x)  "d"x + int_0^"a" "f"("a" - x)  "d"x`

  • True

  • False

Q.3 | Q 6

State whether the following statement is True or False:

`int_(-5)^5 x/(x^2 + 7)  "d"x` = 10

  • True

  • False

Q.4

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 1.6 Definite Integration Q.4

Solve the following [3 Marks]

Q.4 | Q 1

Evaluate `int_0^1 (x^2 + 3x + 2)/sqrt(x)  "d"x`

Q.4 | Q 2

Evaluate `int_0^1 1/(sqrt(1 + x) + sqrt(x))  "d"x`

Q.4 | Q 3

If `int_0^"a" (2x + 1)  "d"x` = 2, find a

Q.4 | Q 4

If `int_1^"a" (3x^2 + 2x + 1)  "d"x` = 11, find the real value of a

Q.4 | Q 5

Evaluate `int_1^"e" 1/(x(1 + log x)^2)  "d"x`

Q.4 | Q 6

Evaluate `int_1^2 1/(x^2 + 6x + 5)  "d"x`

Q.4 | Q 7

Evaluate `int_1^2 (3x)/((9x^2 - 1))  "d"x`

Q.4 | Q 8

Evaluate the following integrals:

`int_1^3 (root(3)(x + 5))/(root(3)(x + 5) + root(3)(9 - x))*dx`

Q.4 | Q 9

Evaluate `int_1^2 (sqrt(x))/(sqrt(3 - x) + sqrt(x))  "d"x`

Q.4 | Q 10

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

Q.5

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 1.6 Definite Integration Q.5

[4 Marks]

Q.5 | Q 1

Evaluate `int_2^3 x/((x + 2)(x + 3))  "d"x`

Q.5 | Q 2

Evaluate `int_1^2 "e"^(2x) (1/x - 1/(2x^2))  "d"x`

Q.5 | Q 3

Evaluate `int_1^3 log x  "d"x`

Q.5 | Q 4

Evaluate `int_1^3 x^2*log x  "d"x`

Q.5 | Q 5

Evaluate `int_0^1 "e"^(x^2)*"x"^3  "d"x`

Q.5 | Q 6

Evaluate `int_0^"a" x^2 ("a" - x)^(3/2)  "d"x`

Q.5 | Q 7

Evaluate `int_0^1 x(1 - x)^5  "d"x`

Q.6

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 1.6 Definite Integration Q.6

Activity [4 Marks]

Q.6 | Q 1

By completing the following activity, Evaluate `int_1^2 (x + 3)/(x(x + 2))  "d"x`

Solution: Let I = `int_1^2 (x + 3)/(x(x + 2))  "d"x`

Let `(x + 3)/(x(x + 2)) = "A"/x + "B"/((x + 2))`

∴ x + 3 = A(x + 2) + B.x

∴ A = `square`, B = `square`

∴ I = `int_1^2[("( )")/x + ("( )")/((x + 2))] "d"x`

∴ I = `[square log x + square log(x + 2)]_1^2`

∴ I = `square`

Q.6 | Q 2

By completing the following activity, Evaluate `int_2^5 (sqrt(x))/(sqrt(x) + sqrt(7 - x))  "d"x`.

Solution: Let I = `int_2^5 (sqrt(x))/(sqrt(x) + sqrt(7 - x))  "d"x`     ......(i)

Using the property, `int_"a"^"b" "f"(x) "d"x = int_"a"^"b" "f"("a" + "b" - x)  "d"x`, we get

I = `int_2^5 ("(  )")/(sqrt(7 - x) + "(  )")  "d"x`   ......(ii)

Adding equations (i) and (ii), we get

2I = `int_2^5 (sqrt(x))/(sqrt(x) - sqrt(7 - x))  "d"x + (   )  "d"x`

2I = `int_2^5 (("(    )" + "(     )")/("(    )" + "(     )"))  "d"x`

2I = `square`

∴ I =  `square`

Solutions for Chapter 1.6: Definite Integration

Q.1Q.2Q.3Q.4Q.5Q.6
SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 1.6 - Definite Integration - Shaalaa.com

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 1.6 - Definite 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 1.6 (Definite 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 1.6 Definite Integration are Fundamental Theorem of Integral Calculus, Properties of Definite Integrals.

Using SCERT Maharashtra Question Bank 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 solutions Definite 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.

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