Lesson 1.08i

1.08i Integration by parts Quiz: OCR Maths, Unit 8

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 1.08i, Integration by parts: 20 multiple choice questions for the OCR Maths (H240), Unit 8: Integration, written with Revision Ninja.

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The 20 questions

  1. In the integration by parts formula, what expression is subtracted from uv?

    • ∫ u (du/dx) dx
    • ∫ v (du/dx) dx
    • ∫ v (dv/dx) dx
    • ∫ u (dv/dx) dx

  2. Integration by parts is derived from which differentiation rule?

    • Quotient rule
    • Chain rule
    • Product rule
    • Power rule

  3. Which is the indefinite integral of ln x with respect to x?

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

  4. What is the indefinite integral of x e^x with respect to x?

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

  5. What type of solution does an indefinite integral represent?

    • Single specific curve
    • Unique function
    • Family of curves
    • Definite value

  6. What is the indefinite integral of x cos x with respect to x?

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

  7. What is the exact value of the definite integral of ln x from x = 1 to x = e?

    • e - 1
    • e
    • 2
    • 1

  8. Find the indefinite integral of x e^(2x) with respect to x.

    • (e^(2x)/4)(2x + 1) + C
    • (e^(2x)/4)(2x - 1) + C
    • (e^(2x)/2)(x - 1) + C
    • x e^(2x) - e^(2x)/2 + C

  9. Find the indefinite integral of x^2 e^x with respect to x.

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

  10. Evaluate the integral of x e^(-x) from x = 0 to x = 1, giving an exact answer.

    • 2/e - 1
    • 1 + 2/e
    • 1 - 2/e
    • 1 - 1/e

  11. Find the indefinite integral of ln(2x) with respect to x.

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

  12. Find the indefinite integral of x cos(3x) with respect to x.

    • (x sin 3x)/3 + (sin 3x)/9 + C
    • x sin 3x + (cos 3x)/3 + C
    • (x sin 3x)/3 + (cos 3x)/9 + C
    • (x sin 3x)/3 - (cos 3x)/9 + C

  13. The area under y = x ln x from x = 1 to x = 2 is closest to which value?

    • 1.386
    • 0.386
    • 0.636
    • 0.886

  14. Find the indefinite integral of x^3 ln x with respect to x.

    • x^4 ln x - x^4/4 + C
    • (x^4 ln x)/4 - x^4/16 + C
    • (x^4 ln x)/4 + x^4/16 + C
    • (x^3 ln x)/3 - x^3/9 + C

  15. A rate of flow is R(t) = t e^(-t) litres per minute. What total volume is supplied from t = 0 to t = infinity?

    • e litres
    • 0.5 litres
    • 1 litre
    • 2 litres

  16. Find the indefinite integral of e^x sin x with respect to x.

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

  17. Evaluate the integral of x sin x from x = 0 to x = pi.

    • pi
    • 2
    • -pi
    • pi/2

  18. Find the indefinite integral of ln x / x^2 with respect to x.

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

  19. Evaluate the integral of x ln x from x = 1 to x = e, giving an exact answer.

    • (e^2 - 1)/4
    • (e^2 + 1)/4
    • e^2/2 + 1/4
    • e^2/4

  20. Find the indefinite integral of x^2 cos x with respect to x.

    • x^2 sin x + 2x cos x + 2 sin x + C
    • x^2 sin x + 2x cos x - 2 sin x + C
    • 2x sin x + x^2 cos x + C
    • x^2 sin x - 2x cos x + 2 sin x + C

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