(i)[6]
Use the substitution $u=\sin 2x$ within an appropriate integral to determine the value of $A$.
(ii)[2]
If $\int_{0}^{k\pi} |\sin^3 2x\cos^3 2x|\,dx=40A$, determine the constant $k$.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
The diagram presents a section of the curve $y=\sin^3 2x\cos^3 2x$. The shaded part shown is enclosed by the curve and the $x$-axis, and its exact area is written as $A$.