Mathematics 9709 · AS & A Level · Integration

Integration — practice question

(a)[3]

Determine the quotient and remainder when $x^4 + 16$ is divided by $x^2 + 4$.

(b)[5]

Hence demonstrate that $\displaystyle \int_{2}^{2\sqrt{3}} \frac{x^4 + 16}{x^2 + 4} \, dx = \frac{4}{3}(\pi + 4)$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Carry out the division to get quotient $x^2+k$.” …