NUST NET Maths chapter 9: Maths · Integration MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

26 exam-style questions on Maths · Integration, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

26 questions · 2 topics · 10 per test

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What chapter 9 covers

Ten Maths · Integration questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. ∫ dx/(2x + 1) equals

  1. A
    (1/2) ln|2x + 1| + c
  2. B
    ln|2x + 1| + c
  3. C
    2 ln|2x + 1| + c
  4. D
    −2/(2x + 1)2 + c
Show answer

Answer: A. d/dx ln|2x + 1| = 2/(2x + 1), so divide by 2: the integral is (1/2) ln|2x + 1| + c.

2. ∫0π sin x dx equals

  1. A
    0
  2. B
    1
  3. C
    2
  4. D
    −2
Show answer

Answer: C. [−cos x] from 0 to π = −cos π + cos 0 = 1 + 1 = 2. Using +cos x as the integral gives −2.

3. ∫ ex(sin x + cos x) dx equals

  1. A
    ex cos x + c
  2. B
    ex sin x + c
  3. C
    ex(sin x − cos x) + c
  4. D
    ex(sin x + cos x) + c
Show answer

Answer: B. Use ∫ ex[f(x) + f′(x)] dx = exf(x) + c with f(x) = sin x, since f′(x) = cos x. Check: d/dx (ex sin x) = ex sin x + ex cos x.

4. The total area between y = x3 and the x-axis from x = −1 to x = 1 is (in square units)

  1. A
    0
  2. B
    1/4
  3. C
    1
  4. D
    1/2
Show answer

Answer: D. The part from −1 to 0 lies below the axis. Each part has area 1/4, so the total is 1/4 + 1/4 = 1/2. ∫−11 x3 dx = 0 only because the signed parts cancel.

5. ∫ (3x2 + 2x) dx equals

  1. A
    6x + 2 + c
  2. B
    x3 + x2 + c
  3. C
    3x3 + 2x2 + c
  4. D
    x3 + 2x2 + c
Show answer

Answer: B. Raise each power by 1 and divide by the new power: 3x3/3 + 2x2/2 = x3 + x2. 6x + 2 is the derivative, not the integral.

6. If ∫14 f(x) dx = 7 and ∫12 f(x) dx = 3, then ∫42 f(x) dx equals

  1. A
    4
  2. B
    −4
  3. C
    10
  4. D
    −10
Show answer

Answer: B. ∫24 f(x) dx = 7 − 3 = 4, and swapping the limits changes the sign, so ∫42 f(x) dx = −4.

7. ∫−11 (x5 + 3x2) dx equals

  1. A
    0
  2. B
    4
  3. C
    1
  4. D
    2
Show answer

Answer: D. x5 is odd, so its integral from −1 to 1 is 0. For the even part, ∫−11 3x2 dx = [x3] from −1 to 1 = 1 − (−1) = 2.

8. ∫ dx/[x(x + 1)] equals

  1. A
    ln|(x + 1)/x| + c
  2. B
    ln|x(x + 1)| + c
  3. C
    ln|x/(x + 1)| + c
  4. D
    ln|x| · ln|x + 1| + c
Show answer

Answer: C. Partial fractions: 1/[x(x + 1)] = 1/x − 1/(x + 1), so the integral is ln|x| − ln|x + 1| = ln|x/(x + 1)| + c.

9. The area under y = ex from x = 0 to x = ln 3 is (in square units)

  1. A
    3
  2. B
    ln 3
  3. C
    2
  4. D
    e3 − 1
Show answer

Answer: C. ∫0ln 3 ex dx = eln 3 − e0 = 3 − 1 = 2. Forgetting the lower limit gives 3.

10. The general solution of dy/dx = 2xy is (A a constant)

  1. A
    y = x2 + A
  2. B
    y = Aex²
  3. C
    y = Ae2x
  4. D
    y = Ax2
Show answer

Answer: B. Separate the variables: dy/y = 2x dx, so ln|y| = x2 + k and y = Aex².

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Ways to practise this chapter

Maths · Integration: questions students ask

How many Maths · Integration MCQs are there?

26, each with the answer and a short explanation, across 2 topics: Methods of integration, Definite integrals and areas. Every chapter test draws ten of them, so you can take it many times.

Is the NUST NET Maths chapter 9 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

Can I read the explanations in Urdu?

Yes. In practice mode and on your results you can switch the explanations to Urdu.

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