Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The function $f$ is given by $f(x) = \frac{2}{(x + 2)^2}$ whenever $x > -2$.
(a)[3]

Calculate $\int_{1}^{\infty} f(x)\,dx$.

(b)[2]

A curve has equation such that $\frac{dy}{dx} = f(x)$. The point $(-1, -1)$ lies on the curve. Find the equation of the curve.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Gives $-2(x+2)^{-1}$, or an equivalent expression” …

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