Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The diagram represents the curve $y = x e^{-ax}$, with $a$ as a positive constant, together with its maximum point $M$.

(a)[4]

Find the exact coordinates for $M$.

(b)[5]

Find the exact value for $\int_0^2 x e^{-ax}\,dx$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use the product rule in a valid way” …