Mathematics 9709 · AS & A Level · Integration

Integration — practice question

(a)[5]

Find the exact value of the integral $\int_{0}^{\frac{\pi}{4}} \sin x\left(4\sin x + 6\cos x\right)\,dx$.

(b)[5]

Given that $\int_{0}^{a} \frac{6}{3x + 2}\,dx = \ln 49$, determine the value of the positive constant $a$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Arrive at $2-2\cos2x$ as part of the integrand” …