Integration by parts

Integration by parts Quiz

Spec 6.2 · Edexcel International A Level Maths: Quiz

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5 questions, one answer each

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  1. 1. Which is the integration by parts formula?

    • A. ∫udvdx dx=uv+∫vdudx dx\int u\frac{dv}{dx}\,dx=uv+\int v\frac{du}{dx}\,dx
    • B. ∫udvdx dx=∫u dx×∫dvdx dx\int u\frac{dv}{dx}\,dx=\int u\,dx\times\int\frac{dv}{dx}\,dx
    • C. ∫udvdx dx=uv−∫vdudx dx\int u\frac{dv}{dx}\,dx=uv-\int v\frac{du}{dx}\,dx
    • D. ∫udvdx dx=dudxdvdx−∫uv dx\int u\frac{dv}{dx}\,dx=\frac{du}{dx}\frac{dv}{dx}-\int uv\,dx

  2. 2. Find ∫xcos⁡x dx\int x\cos x\,dx.

    • A. xsin⁡x+cos⁡x+cx\sin x+\cos x+c
    • B. xsin⁡x−cos⁡x+cx\sin x-\cos x+c
    • C. x22sin⁡x+c\frac{x^2}{2}\sin x+c
    • D. −xsin⁡x+cos⁡x+c-x\sin x+\cos x+c

  3. 3. Find ∫1eln⁡x dx\int_1^e\ln x\,dx.

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

  4. 4. For ∫x2ln⁡x dx\int x^2\ln x\,dx, which is the best choice of uu?

    • A. u=x2u=x^2
    • B. u=ln⁡xu=\ln x
    • C. u=x2ln⁡xu=x^2\ln x
    • D. u=1xu=\frac1x

  5. 5. After two applications for I=∫exsin⁡x dxI=\int e^{x}\sin x\,dx you reach I=exsin⁡x−excos⁡x−II=e^{x}\sin x-e^{x}\cos x-I. What is II?

    • A. ex(sin⁡x−cos⁡x)+ce^{x}(\sin x-\cos x)+c
    • B. 00
    • C. 12ex(sin⁡x+cos⁡x)+c\frac12e^{x}(\sin x+\cos x)+c
    • D. 12ex(sin⁡x−cos⁡x)+c\frac12e^{x}(\sin x-\cos x)+c

Quiz