Mathematics 9709 · AS & A Level · Integration

Integration — practice question

Define $I = \displaystyle\int_{1}^{4} \dfrac{(\sqrt{x}) - 1}{2(x + \sqrt{x})} \, dx$.

(a)[3]

By using the substitution $u = \sqrt{x}$, show that $I = \displaystyle\int_{1}^{2} \dfrac{u - 1}{u + 1} \, du$.

(b)[6]

Hence show that $I = 1 + \ln \dfrac{4}{9}$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State or indicate $du=\dfrac{1}{2\sqrt{x}}dx$” …