(a)[4]
Show that $\displaystyle \int_{2}^{18} \frac{3}{2x} \, dx$ equals $\ln 27$.
(b)[5]
Find the exact value of $\displaystyle \int_{0}^{\frac{\pi}{6}} 4 \sin^2\left( \frac{3}{2}x \right) \, dx$. Show all essential working.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Obtain any of $\tfrac12\ln x$, $\tfrac12\ln(2x)$, or $\tfrac12\ln(kx)$” …
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