Integration using partial fractions

Integration using partial fractions Quiz

Spec H6 · AQA A-Level Maths: Quiz

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5 questions, one answer each

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  1. 1. Find AA if 7(x+1)(x+2)≡Ax+1+Bx+2\frac{7}{(x+1)(x+2)}\equiv\frac{A}{x+1}+\frac{B}{x+2}.

    • A. A=7A=7
    • B. A=−7A=-7
    • C. A=72A=\frac72
    • D. A=1A=1

  2. 2. Find ∫3x+4 dx\int\frac{3}{x+4}\,dx.

    • A. 3ln⁡∣x+4∣+c3\ln|x+4|+c
    • B. 32ln⁡∣x+4∣+c\frac{3}{2}\ln|x+4|+c
    • C. −3(x+4)2+c-\frac{3}{(x+4)^2}+c
    • D. 3ln⁡∣x∣+c3\ln|x|+c

  3. 3. Find ∫63x−2 dx\int\frac{6}{3x-2}\,dx.

    • A. 6ln⁡∣3x−2∣+c6\ln|3x-2|+c
    • B. 2ln⁡∣3x−2∣+c2\ln|3x-2|+c
    • C. 18ln⁡∣3x−2∣+c18\ln|3x-2|+c
    • D. 12ln⁡∣3x−2∣+c\frac12\ln|3x-2|+c

  4. 4. Evaluate ∫13(1x−1x+1)dx\int_1^3\left(\frac1x-\frac1{x+1}\right)dx as a single logarithm.

    • A. ln⁡23\ln\frac23
    • B. ln⁡43\ln\frac43
    • C. ln⁡32\ln\frac32
    • D. ln⁡6\ln6

  5. 5. 1(x−1)(x+1)≡Ax−1+Bx+1\frac{1}{(x-1)(x+1)}\equiv\frac{A}{x-1}+\frac{B}{x+1}. Then ∫231(x−1)(x+1)dx=\int_2^3\frac{1}{(x-1)(x+1)}dx=

    • A. 12ln⁡32\frac12\ln\frac32
    • B. ln⁡32\ln\frac32
    • C. 12ln⁡23\frac12\ln\frac23
    • D. 12ln⁡3\frac12\ln3

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