Integration by parts

Integration by parts Quiz

Spec 8.5 · Edexcel A-Level Maths: Quiz

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5 questions, one answer each

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  1. 1. Find ∫xcos⁡x dx\int x\cos x\,\mathrm{d}x.

    • A. xsin⁡x−cos⁡x+cx\sin x-\cos x+c
    • B. −xsin⁡x+cos⁡x+c-x\sin x+\cos x+c
    • C. sin⁡x−xcos⁡x+c\sin x-x\cos x+c
    • D. xsin⁡x+cos⁡x+cx\sin x+\cos x+c

  2. 2. Which choice of uu is best for ∫xln⁡x dx\int x\ln x\,\mathrm{d}x?

    • A. u=ln⁡xu=\ln x
    • B. u=xu=x
    • C. u=xln⁡xu=x\ln x
    • D. u=1u=1

  3. 3. Evaluate ∫01xe−x dx\int_0^1xe^{-x}\,\mathrm{d}x.

    • A. 11
    • B. 1−1e1-\frac1e
    • C. 1−2e1-\frac2e
    • D. 2e−1\frac2e-1

  4. 4. How many times must integration by parts be applied to ∫x3ex dx\int x^3e^x\,\mathrm{d}x?

    • A. 22
    • B. 33
    • C. 44
    • D. 11

  5. 5. Find ∫2xln⁡x dx\int2x\ln x\,\mathrm{d}x.

    • A. x2ln⁡x+cx^2\ln x+c
    • B. x2ln⁡x−x+cx^2\ln x-x+c
    • C. 2ln⁡x+2+c2\ln x+2+c
    • D. x2ln⁡x−x22+cx^2\ln x-\frac{x^2}{2}+c

Quiz