Integration by substitution

Integration by substitution Quiz

Spec H5 · AQA A-Level Maths: Quiz

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5 questions, one answer each

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  1. 1. Find ∫2x ex2dx\int2x\,e^{x^2}dx.

    • A. ex2+ce^{x^2}+c
    • B. 2ex2+c2e^{x^2}+c
    • C. x2ex2+cx^2e^{x^2}+c
    • D. ex22+c\frac{e^{x^2}}{2}+c

  2. 2. Using u=x2+1u=x^2+1, ∫01x(x2+1)2dx\int_0^1 x(x^2+1)^2dx becomes:

    • A. ∫12u2 du\int_1^2u^2\,du
    • B. 12∫12u2 du\frac12\int_1^2u^2\,du
    • C. 12∫01u2 du\frac12\int_0^1u^2\,du
    • D. 2∫12u2 du2\int_1^2u^2\,du

  3. 3. Find ∫2xx2+3 dx\int\frac{2x}{x^2+3}\,dx.

    • A. ln⁡(x2+3)+c\ln(x^2+3)+c
    • B. 1x2+3+c\frac{1}{x^2+3}+c
    • C. 2ln⁡(x2+3)+c2\ln(x^2+3)+c
    • D. x2x2+3+c\frac{x^2}{x^2+3}+c

  4. 4. Find ∫cos⁡xsin⁡4x dx\int\cos x\sin^4x\,dx.

    • A. cos⁡2x2+c\frac{\cos^2x}{2}+c
    • B. sin⁡5x+c\sin^5x+c
    • C. −sin⁡5x5+c-\frac{\sin^5x}{5}+c
    • D. sin⁡5x5+c\frac{\sin^5x}{5}+c

  5. 5. Evaluate ∫03xx+1 dx\int_0^{3}\frac{x}{\sqrt{x+1}}\,dx using u=x+1u=x+1.

    • A. 43\frac43
    • B. 22
    • C. 83\frac83
    • D. 163\frac{16}{3}

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