Integration as the reverse of differentiation

Integration as the reverse of differentiation Quiz

Spec 8.1–2 · Edexcel A-Level Maths: Quiz

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5 questions, one answer each

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  1. 1. Find ∫6x2 dx\int6x^{2}\,dx.

    • A. 12x+c12x+c
    • B. 2x3+c2x^{3}+c
    • C. 6x3+c6x^{3}+c
    • D. 3x3+c3x^{3}+c

  2. 2. Find ∫x−3 dx\int x^{-3}\,dx.

    • A. −3x−4+c-3x^{-4}+c
    • B. 12x−2+c\frac12x^{-2}+c
    • C. x−2+cx^{-2}+c
    • D. −12x−2+c-\frac12x^{-2}+c

  3. 3. Find ∫x dx\int\sqrt x\,dx.

    • A. 23x3/2+c\frac23x^{3/2}+c
    • B. 12x−1/2+c\frac12x^{-1/2}+c
    • C. 32x3/2+c\frac32x^{3/2}+c
    • D. x3/2+cx^{3/2}+c

  4. 4. Find ∫(2x+1)(x−3) dx\int(2x+1)(x-3)\,dx.

    • A. 4x−5+c4x-5+c
    • B. 23x3−52x2−3+c\frac23x^{3}-\frac52x^{2}-3+c
    • C. 23x3−52x2−3x+c\frac23x^{3}-\frac52x^{2}-3x+c
    • D. (x2+x)(x22−3x)+c\left(x^{2}+x\right)\left(\frac{x^{2}}{2}-3x\right)+c

  5. 5. f′(x)=2x−3f'(x)=2x-3 and f(1)=0f(1)=0. Find f(x)f(x).

    • A. x2−3xx^{2}-3x
    • B. x2−3x+2x^{2}-3x+2
    • C. x2−3x−2x^{2}-3x-2
    • D. 2x2−3x+12x^{2}-3x+1

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