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Indefinite Integrals MCQs With Answers | Class 12 Math Notes Study Material Download Free PDF

 

MCQs on Class 12 Maths Chapter 7 Integrals

Check out the MCQs for Class 12 Maths Chapter 7 Integrals. Each MCQ is provided with four options, out of which only one option is correct. Students should choose the correct option and cross-verify their answers to the solutions provided on our page. Also, check important questions for class 12 Maths.

1) If (d/dx) f(x) is g(x), then the antiderivative of g(x) is

  1. f(x)
  2. f’(x)
  3. g’(x)
  4. None of the above

Answer: (a) f(x)

Given: (d/dx) f(x) = g(x)

We know that the integration is the inverse process of differentiation, then the antiderivative of g(x) is f(x).

Hence, option (a) f(x) is the correct answer.

2) 0∫2 x2 dx =

  1. 2
  2. ⅔
  3. 8/3
  4. None of these

Answer: (c) 8/3

Explanation: 0∫2 x2 dx = [x3/3]02

Now, apply the limits, we get

0∫2 x2 dx =(23/3) – 0 = 8/3

Hence, option (c) is the correct answer.

3) 0∫2 (x2 + 3)dx equals

  1. 24/3
  2. 25/3
  3. 26/3
  4. None of the above.

Answer: (c) 26/3

0∫2 (x2 + 3)dx = [(x3/3)+ 3x]02

0∫2 (x2 + 3)dx = [(23/3)+ 3(2)] – 0 = (8/3)+6 = (8+18)/3 = 26/3.

Hence, option (c) 26/3 is the correct answer.

4) If ∫ 2x dx = f(x) + C, then f(x) is

  1. 2x
  2. 2x loge2
  3. 2x / loge2
  4. 2x+1/x+1

Answer: (c) 2x / loge2

Explanation: We know that differentiation is the inverse process of integration.

Therefore, (d/dx)(2x / loge2) = (1/loge2).2x. loge2 = 2x.

Hence, option (c) is the correct answer.

5) 1∫2 dx/x2 equals

  1. 1
  2. -1
  3. 2
  4. ½

Answer: (d) ½

1∫2 dx/x2 = 1∫2 x-2 dx = [x-1/-1]12

Now, apply limits, we get

1∫2 dx/x2 = (2-1/-1) – (1-1/-1)

1∫2 dx/x2 = (1/-2)+1 = (1-2)/-2= -1/-2 = ½

Hence, 1∫2 dx/x2 = ½.

6) ∫cot²x dx equals to

  1. cot x – x + C
  2. -cot x – x + C
  3. cot x + x + C
  4. -cot x + x + C

Answer: (b) -cot x – x + C

Explanation:

We know that cot2 x = cosec2x – 1

∫cot²x dx = ∫ (cosec2x – 1) dx = -cot x -x + C. [Since, ∫cosec2x dx = -cot x + c]

Hence, the correct answer is option (b) -cot x – x + C.

7) 0∫Ï€ sin2 x dx =

  1. π/2
  2. π/4
  3. 2Ï€
  4. 4Ï€

Answer: (a) Ï€/2

Explanation: 0∫Ï€ sin2 x dx = (½) 0∫Ï€ (1-cos2x) dx

Now, integrate the function and apply the limits, we get

0∫Ï€ sin2 x dx = (½) ( Ï€-0) = Ï€/2.

Hence, option (a) π/2 is the correct answer.

8) 0∫4 3x dx equals

  1. 12
  2. 24
  3. 48
  4. 86

Answer: (b) 24

Explanation:

0∫4 3x dx = 30∫4 x dx = 3[x2/2]04

Now, apply the limits, we get

0∫4 3x dx = 3[(42/2) -0]

0∫4 3x dx = 3[8-0] = 24

Hence, 0∫4 3x dx = 24.

9) Integrate 0∫2 (x2+x+1) dx

  1. 15/2
  2. 20/5
  3. 20/3
  4. 3/20

Answer: (c) 20/3

Explanation:

0∫2 (x2+x+1) dx = [(x3/3)+(x2/2) +x]02

0∫2 (x2+x+1) dx = [(23/3) + (22/2) + 2] – 0

0∫2 (x2+x+1) dx = (8/3) + 2+2 = (8/3)+4

0∫2 (x2+x+1) dx = (8+12)/3 = 20/3.

Hence, option (c) 20/3 is the correct answer.

10) If ∫ sec²(7 – 4x)dx = a tan (7 – 4x) + C, then value of a is

  1. -4
  2. -¼
  3. 3
  4. 7

Answer: (b) -¼

Explanation:

Given: ∫ sec²(7 – 4x)dx = a tan (7 – 4x) + C

∫ sec²(7 – 4x)dx ={[tan (7-4x)]/-4} + C

∫ sec²(7 – 4x)dx = (-¼) tan (7-4x) + C

Hence, the value of a is -¼.

Class 12 Maths Chapter 7 Integrals MCQs are available online to help students to score good marks in the examination. The multiple-choice questions are framed as per the CBSE syllabus and NCERT guidelines. These MCQs are provided with answers and detailed explanations.

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