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 2021 chapter 2 - Definite Integration [Latest edition]

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12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2021 - Shaalaa.com

Chapter 2: Definite Integration

Q.1Q.2Q.3Q.4Q.5Q.6
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Q.1

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2021 Chapter 2 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

Choose the correct alternative:

`int_0^2 "e"^x  "d"x` =

  • 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

Choose the correct alternative:

`int_"a"^"b" "f"(x)  "d"x` =

  • `int_"b"^"a" "f"(x)  "d"x`

  • `- int_"b"^"a" "f"(x)  "d"x`

  • `- int_"b"^"a" "f"(x)  "d"x`

  • `int_0^"a" "f"(x)  "d"x`

Q.1 | Q 8

Choose the correct alternative:

`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 2021 Chapter 2 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)  "d"x` = ______

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 2021 Chapter 2 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 2021 Chapter 2 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 `int_1^3 (root(3)(x + 5))/(root(3)(x + 5) + root(3)(9 - x))  "d"x`

Q.4 | Q 9

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

Q.4 | Q 10

Evaluate `int_0^1 log(1 / x - 1)  "d"x`

Q.5

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2021 Chapter 2 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 2021 Chapter 2 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`

Chapter 2: Definite Integration

Q.1Q.2Q.3Q.4Q.5Q.6
12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2021 - Shaalaa.com

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2021 chapter 2 - Definite Integration

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2021 chapter 2 (Definite 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 2021 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 2021 chapter 2 Definite Integration are Fundamental Theorem of Integral Calculus, Properties of Definite Integrals.

Using SCERT Maharashtra Question Bank 12th Board Exam solutions Definite 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 Definite Integration 12th Board Exam extra questions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2021 and can use Shaalaa.com to keep it handy for your exam preparation

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