(a)[4]
Show that $f'(x) < 0$ for each $x$ satisfying $-\tfrac{1}{2}\pi < x < \tfrac{3}{2}\pi$.
(b)[4]
Find $\int_{\frac{\pi}{6}}^{2\pi} f(x) \, dx$. Give your answer in a fully simplified exact form.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
Define $f(x) = \dfrac{\cos x}{1 + \sin x}$.