Lesson H5

H5 Integration by substitution and by parts Quiz: AQA Maths, Unit 8

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson H5, Integration by substitution and by parts: 20 multiple choice questions for the AQA Maths (7357), Unit 8: Integration, written with Revision Ninja.

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The 20 questions

  1. What is the formula for integration by parts?

    • integral of u dv = u integral of v dx - integral of v du
    • integral of u dv = uv - integral of v du
    • integral of u dv = u/v - integral of v du
    • integral of u dv = uv + integral of v du

  2. Integration by parts is the inverse of which differentiation rule?

    • The chain rule
    • The power rule
    • The quotient rule
    • The product rule

  3. Integration by substitution is the inverse of which differentiation rule?

    • The quotient rule
    • The chain rule
    • The sum rule
    • The product rule

  4. Which is an integral of 2x(x^2 + 1)^3 with respect to x?

    • (x^2 + 1)^3/3 + C
    • (x^2 + 1)^4 + C
    • (x^2 + 1)^4/2 + C
    • (x^2 + 1)^4/4 + C

  5. Which is an integral of x e^(x^2) with respect to x?

    • x^2 e^(x^2)/2 + C
    • e^(x^2)/2 + C
    • e^(x^2) + C
    • 2e^(x^2) + C

  6. Using integration by parts with u = x and dv/dx = e^x, what is the integral of x e^x dx?

    • e^x + C
    • x e^x + e^x + C
    • x^2 e^x/2 + C
    • x e^x - e^x + C

  7. Using integration by parts with u = ln x, what is the integral of ln x dx?

    • x ln x + x + C
    • 1/x + C
    • x ln x - x + C
    • (ln x)/x + C

  8. What is the value of the integral from 0 to 1 of x e^x dx?

    • 2e - 1
    • e - 1
    • 1
    • e

  9. Which is an integral of 3x^2 (x^3 - 1)^2 with respect to x?

    • (x^3 - 1)^2/2 + C
    • (x^3 - 1)^3 + C
    • (x^3 - 1)^3/3 + C
    • x^3 (x^3 - 1)^3/3 + C

  10. What is the value of the integral from 0 to 1 of 2x/(x^2 + 1) dx?

    • 2 ln 2
    • ln 1
    • 1/2
    • ln 2

  11. Which is an integral of x cos x with respect to x?

    • -x sin x + cos x + C
    • x sin x + sin x + C
    • x sin x + cos x + C
    • x sin x - cos x + C

  12. Which is an integral of x^2 (x^3 + 5)^4 with respect to x?

    • x^3 (x^3 + 5)^5/15 + C
    • (x^3 + 5)^5/15 + C
    • (x^3 + 5)^5/5 + C
    • (x^3 + 5)^4/12 + C

  13. Which is an integral of x^2 e^x with respect to x?

    • e^x (x^2 - 2x + 2) + C
    • e^x (x^2 - 2x) + C
    • e^x (x^2 + 2x + 2) + C
    • 2x e^x + C

  14. What is the value of the integral from 0 to pi/2 of x sin x dx?

    • pi/2 - 1
    • pi/2 + 1
    • pi/2
    • 1

  15. What is the value of the integral from 0 to 1 of x(1 - x^2)^3 dx?

    • 1/2
    • -1/8
    • 1/4
    • 1/8

  16. Which is an integral of (ln x)/x^2 with respect to x, for x > 0?

    • (ln x)/x + C
    • -(ln x - 1)/x + C
    • -(ln x + 1)/x + C
    • (ln x + 1)/x + C

  17. Which is an integral of x^3 e^(x^2) with respect to x?

    • (x^2 - 1) e^(x^2) + C
    • x^2 e^(x^2)/2 + C
    • (1/2)(x^2 + 1) e^(x^2) + C
    • (1/2)(x^2 - 1) e^(x^2) + C

  18. Which is an integral of x ln x with respect to x, for x > 0?

    • (x^2/2) ln x - x/2 + C
    • x^2 ln x - x^2/2 + C
    • (x^2/2) ln x + x^2/4 + C
    • (x^2/2) ln x - x^2/4 + C

  19. Which is an integral of 1/(x ln x) with respect to x, for x > 1?

    • ln x + C
    • ln|ln x| + C
    • 1/ln x + C
    • -1/(ln x)^2 + C

  20. Which is an integral of e^x sin x with respect to x?

    • (e^x/2)(cos x - sin x) + C
    • e^x (sin x - cos x) + C
    • (e^x/2)(sin x - cos x) + C
    • (e^x/2)(sin x + cos x) + C

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