(i)[5]
Show that $(2 \sin x + \cos x)^2$ may be expressed as $\frac{5}{2} + 2 \sin 2x - \frac{3}{2} \cos 2x$.
(ii)[4]
Hence find the exact result of $\int_0^{\frac{1}{4}\pi} (2 \sin x + \cos x)^2 \, dx$.
Mathematics 9709 · AS & A Level · Integration
Mathematics 9709 · AS & A Level · Integration
Show that $(2 \sin x + \cos x)^2$ may be expressed as $\frac{5}{2} + 2 \sin 2x - \frac{3}{2} \cos 2x$.
Hence find the exact result of $\int_0^{\frac{1}{4}\pi} (2 \sin x + \cos x)^2 \, dx$.