(a)[3]
Find the exact value of $f'\left(\tfrac{3\pi}{7}\right)$.
(b)[4]
Determine the exact value of $\displaystyle \int_{0}^{\frac{1}{2}\pi} \left(f(x) + \sin x\right)\,dx$.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
The function $f$ is given by $f(x)=\tan^2\left(\tfrac{1}{2}x\right)$, with domain $0 \leq x < \pi$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate so that the result is in the form $k\tan\tfrac{1}{2}x\sec^2\tfrac{1}{2}x$.” …
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