Mathematics 9709 · AS & A Level · Integration

Integration — practice question

Define $f(x) = \frac{1}{(9 - x)\sqrt{x}}$.

(a)[4]

Determine the $x$-coordinate of the stationary point on the curve given by $y = f(x)$.

(b)[6]

With the substitution $u = \sqrt{x}$, show that $\int_{0}^{4} f(x)\,dx = \frac{1}{3}\ln 5$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply the quotient rule or the product rule” …