(a)[2]
Show that the value of $\int_0^{\pi} \cos 2x \, dx$ is $\frac{1}{2}$.
(b)[4]
Using a suitable trigonometric identity, find the exact value of $\int_{\frac{\pi}{6}}^{\frac{5\pi}{6}} 3\tan^2 x \, dx$.
Mathematics 9709 · AS & A Level · Integration
Show that the value of $\int_0^{\pi} \cos 2x \, dx$ is $\frac{1}{2}$.
Using a suitable trigonometric identity, find the exact value of $\int_{\frac{\pi}{6}}^{\frac{5\pi}{6}} 3\tan^2 x \, dx$.
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Obtain an integral $a\sin 2x$ for $a=\pm1,\ 2$ or $\tfrac12$” …