Improper integrals

Improper integrals Quiz

Spec E1 · AQA A-Level Further Maths: Quiz

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5 questions, one answer each

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  1. 1. Find ∫1∞1x2 dx\int_1^\infty\dfrac{1}{x^2}\,dx.

    • A. 12\dfrac12
    • B. 11
    • C. 22
    • D. The integral diverges

  2. 2. Find ∫01x−1/2 dx\int_0^1x^{-1/2}\,dx.

    • A. 12\dfrac12
    • B. 11
    • C. 22
    • D. The integral diverges

  3. 3. What is lim⁡x→0+xln⁡x\displaystyle\lim_{x\to0^+}x\ln x?

    • A. −∞-\infty
    • B. −1-1
    • C. 11
    • D. 00

  4. 4. Find ∫0∞e−2x dx\int_0^\infty\mathrm{e}^{-2x}\,dx.

    • A. 12\dfrac12
    • B. 22
    • C. 11
    • D. The integral diverges

  5. 5. Which of these integrals diverges?

    • A. ∫1∞x−2 dx\displaystyle\int_1^\infty x^{-2}\,dx
    • B. ∫1∞x−3 dx\displaystyle\int_1^\infty x^{-3}\,dx
    • C. ∫1∞x−1/2 dx\displaystyle\int_1^\infty x^{-1/2}\,dx
    • D. ∫01x−1/2 dx\displaystyle\int_0^1x^{-1/2}\,dx

Quiz