Inverse trigonometric functions: differentiation and integration

Inverse trigonometric functions: differentiation and integration Quiz

Spec E5–E6 · AQA A-Level Further Maths: Quiz

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  1. 1. Differentiate arcsin⁡(2x)\arcsin(2x).

    • A. 11−4x2\dfrac{1}{\sqrt{1-4x^2}}
    • B. 21−4x2\dfrac{2}{\sqrt{1-4x^2}}
    • C. 21−2x2\dfrac{2}{\sqrt{1-2x^2}}
    • D. −21−4x2-\dfrac{2}{\sqrt{1-4x^2}}

  2. 2. Find ∫1x2+9 dx\displaystyle\int\frac{1}{x^2+9}\,dx.

    • A. arctan⁡x3+c\arctan\dfrac x3+c
    • B. 3arctan⁡x3+c3\arctan\dfrac x3+c
    • C. 13arctan⁡x3+c\dfrac13\arctan\dfrac x3+c
    • D. 19arctan⁡x3+c\dfrac19\arctan\dfrac x3+c

  3. 3. Find ∫0311+x2 dx\displaystyle\int_0^{\sqrt3}\frac{1}{1+x^2}\,dx.

    • A. π6\dfrac\pi6
    • B. π4\dfrac\pi4
    • C. π2\dfrac\pi2
    • D. π3\dfrac\pi3

  4. 4. Which substitution suits ∫9−x2 dx\displaystyle\int\sqrt{9-x^2}\,dx?

    • A. x=3sin⁡θx=3\sin\theta
    • B. x=3tan⁡θx=3\tan\theta
    • C. x=9sin⁡θx=9\sin\theta
    • D. x=sin⁡θ3x=\dfrac{\sin\theta}{3}

  5. 5. Differentiate arccos⁡x\arccos x.

    • A. 11+x2\dfrac{1}{1+x^2}
    • B. 11−x2\dfrac{1}{\sqrt{1-x^2}}
    • C. −11−x2-\dfrac{1}{\sqrt{1-x^2}}
    • D. −11−x2-\dfrac{1}{1-x^2}

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