Inverse trigonometric functions: differentiation and integrationEdexcel A-Level Further Maths: Mind map

Exam questions on Inverse trigonometric functions: differentiation and integration

1. Let $f(x)=\frac12\arctan\left(x^2\right)$.
   Hence find the exact value of $\int_0^1\frac{x}{1+x^4}\,dx$.2 marks
2. Let $y=\arcsin x+x\sqrt{1-x^2}$ for $-1<x<1$.
   Hence find the exact value of $\int_0^{1/2}\sqrt{1-x^2}\,dx$.2 marks
3. Let $f(x)=\frac{1}{\sqrt{9-4x^2}}$ and $g(x)=\frac{1}{9+4x^2}$.
   Use the substitution $x=\frac32\sin\theta$ to show that $\int_0^{3/4}f(x)\,dx=\frac\pi{12}$.3 marks