Inverse trigonometric functions: differentiation and integration

Inverse trigonometric functions: differentiation and integration Quiz

Spec 5.5–6 · Edexcel A-Level Further Maths: Quiz

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5 questions, one answer each

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1. Differentiate $\arcsin(2x)$ .
- A. $\frac{1}{\sqrt{1-4x^2}}$
- B. $\frac{2}{\sqrt{1-4x^2}}$
- C. $\frac{2}{\sqrt{1-x^2}}$
- D. $\frac{1}{2\sqrt{1-4x^2}}$
2. Find $\int_0^{1/2}\frac{1}{\sqrt{1-x^2}}\,dx$ .
- A. $\frac\pi3$
- B. $\frac\pi4$
- C. $\frac\pi2$
- D. $\frac\pi6$
3. Differentiate $\arctan(3x)$ .
- A. $\frac{3}{1+9x^2}$
- B. $\frac{1}{1+9x^2}$
- C. $\frac{3}{1+3x^2}$
- D. $\frac{1}{3(1+x^2)}$
4. Which substitution suits $\int\sqrt{9-x^2}\,dx$ ?
- A. $x=9\sin\theta$
- B. $x=3\tan\theta$
- C. $x=3\sin\theta$
- D. $x=\sin3\theta$
5. Find $\int_0^2\frac{1}{4+x^2}\,dx$ .
- A. $\frac\pi4$
- B. $\frac\pi8$
- C. $\frac\pi2$
- D. $\frac\pi{16}$