Hyperbolic and trigonometric substitutions

Hyperbolic and trigonometric substitutions Quiz

Spec 4.3–4 · Edexcel International A Level Further Maths: Quiz

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5 questions, one answer each

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  1. 1. Find ∫dx4+x2\int\frac{dx}{4+x^2}.

    • A. arctan⁡x2+c\arctan\frac x2+c
    • B. 2arctan⁡x2+c2\arctan\frac x2+c
    • C. 12arctan⁡x2+c\frac12\arctan\frac x2+c
    • D. 14arctan⁡x2+c\frac14\arctan\frac x2+c

  2. 2. Find ∫dxx2+25\int\frac{dx}{\sqrt{x^2+25}}.

    • A. 15arsinh⁡x5+c\frac15\operatorname{arsinh}\frac x5+c
    • B. arcsin⁡x5+c\arcsin\frac x5+c
    • C. arcosh⁡x5+c\operatorname{arcosh}\frac x5+c
    • D. arsinh⁡x5+c\operatorname{arsinh}\frac x5+c

  3. 3. Find ∫dx9−x2\int\frac{dx}{\sqrt{9-x^2}}.

    • A. arcsin⁡x3+c\arcsin\frac x3+c
    • B. arsinh⁡x3+c\operatorname{arsinh}\frac x3+c
    • C. 13arcsin⁡x3+c\frac13\arcsin\frac x3+c
    • D. 3arcsin⁡x3+c3\arcsin\frac x3+c

  4. 4. Which substitution simplifies x2−9\sqrt{x^2-9}?

    • A. x=3sinh⁡ux=3\sinh u
    • B. x=3cosh⁡ux=3\cosh u
    • C. x=3tan⁡θx=3\tan\theta
    • D. x=9sin⁡θx=9\sin\theta

  5. 5. Find ∫dxx2+4x+13\int\frac{dx}{x^2+4x+13}.

    • A. arctan⁡(x+2)+c\arctan(x+2)+c
    • B. 12arctan⁡x+23+c\frac12\arctan\frac{x+2}{3}+c
    • C. 13arctan⁡x+23+c\frac13\arctan\frac{x+2}{3}+c
    • D. 13arctan⁡x3+c\frac13\arctan\frac{x}{3}+c

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