(a)[3]
Determine the exact value of $f'\left(\frac{3}{2}\pi\right)$.
(b)[4]
Determine the exact value of $\int_0^{\frac{\pi}{2}} \left(f(x) + \sin x\right) \, dx$.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
The function $f$ is given by $f(x) = \tan^2\left(\frac{1}{2}x\right)$ for $0 \leq x < \pi$.
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This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate so as to obtain a form $k\tan \frac{1}{2}x\sec^2 \frac{1}{2}x$” …
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