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 ∫ 2^x dx = f(x) + C, then f(x) is

1. 2^x
2. 2^x log_e2
3. 2^x / log_e2
4. 2^x+1/x+1

Answer: (c) 2^x / log_e2

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

Therefore, (d/dx)(2^x / log_e2) = (1/log_e2).2^x. log_e2 = 2^x.

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∫^π sin² x dx =

1. π/2
2. π/4
3. 2π
4. 4π

Answer: (a) π/2

Explanation: ₀∫^π sin² x dx = (½) ₀∫^π (1-cos2x) dx

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

₀∫^π sin² x dx = (½) ( π-0) = π/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.