(i)[4]
By expanding $\sin(2x + x)$ first, show that $\sin 3x = 3\sin x - 4\sin^3 x$.
(ii)[4]
Hence, with all necessary working shown, find the exact value of $\int_{0}^{\frac{1}{3}\pi} \sin^3 x\, dx$.
Mathematics 9709 · AS & A Level · Integration
Mathematics 9709 · AS & A Level · Integration
By expanding $\sin(2x + x)$ first, show that $\sin 3x = 3\sin x - 4\sin^3 x$.
Hence, with all necessary working shown, find the exact value of $\int_{0}^{\frac{1}{3}\pi} \sin^3 x\, dx$.