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

Exam questions on Inverse trigonometric functions: differentiation and integration

1. Let $\mathrm{f}(x)=\arctan(3x)$.
   Find the equation of the tangent to the curve $y=\mathrm{f}(x)$ at the point where $x=\dfrac13$.2 marks
2. The curve $C$ has equation $y=\arccos\left(\dfrac{x}{2}\right)$ for $-2\le x\le2$.
   Find the values of $x$ for which the gradient of $C$ is undefined, and describe the tangent to $C$ at these points.2 marks
3. Let $I=\int_0^1\dfrac{1}{\sqrt{4-x^2}}\,dx$ and $J=\int_0^1\sqrt{4-x^2}\,dx$.
   Find the exact value of $I$.3 marks