Mathematics 9709 · AS & A Level · Integration

Integration — practice question

(a)[4]

By using the substitution $u = \cos x$, show that $\int_{0}^{\pi} \sin 2x\, e^{2\cos x}\, dx = \int_{-1}^{1} 2u e^{2u}\, du$.

(b)[4]

Hence determine the exact value of $\int_0^\pi \sin 2x\, e^{2\cos x}\, dx$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State that $\frac{du}{dx}=-\sin x$” …