Integration by parts

Integration by parts Quiz

Spec H5 · AQA A-Level Maths: Quiz

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5 questions, one answer each

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  1. 1. For ∫xsin⁡x dx\int x\sin x\,dx the best choice is:

    • A. u=x, dvdx=sin⁡xu=x,\ \frac{dv}{dx}=\sin x
    • B. u=sin⁡x, dvdx=xu=\sin x,\ \frac{dv}{dx}=x
    • C. u=xsin⁡x, dvdx=1u=x\sin x,\ \frac{dv}{dx}=1
    • D. u=1, dvdx=xsin⁡xu=1,\ \frac{dv}{dx}=x\sin x

  2. 2. Find ∫xsin⁡x dx\int x\sin x\,dx.

    • A. xcos⁡x−sin⁡x+cx\cos x-\sin x+c
    • B. −xcos⁡x+sin⁡x+c-x\cos x+\sin x+c
    • C. −xcos⁡x−sin⁡x+c-x\cos x-\sin x+c
    • D. −x22cos⁡x+c-\frac{x^2}{2}\cos x+c

  3. 3. Find ∫xex dx\int xe^{x}\,dx.

    • A. (x−1)ex+c(x-1)e^x+c
    • B. (x+1)ex+c(x+1)e^x+c
    • C. xex+cxe^x+c
    • D. x22ex+c\frac{x^2}{2}e^x+c

  4. 4. Evaluate ∫1eln⁡x dx\int_1^e\ln x\,dx.

    • A. e−1e-1
    • B. 00
    • C. 11
    • D. ee

  5. 5. The result of ∫x2ex dx\int x^2e^{x}\,dx is x2ex−∫…x^2e^x-\int\dots. The remaining integral is:

    • A. ∫x3ex dx\int x^3e^x\,dx
    • B. ∫2ex dx\int2e^x\,dx
    • C. ∫x33ex dx\int\frac{x^3}{3}e^x\,dx
    • D. ∫2xex dx\int2xe^x\,dx

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