Question Detail

To integrate (\sin^2 x), use the trigonometric identity (\sin^2 x = \frac{1 - \cos 2x}{2}).(\int \sin^2 x\,dx = \int \frac{1 - \cos 2x}{2}\,dx)(= \frac{1}{2} \int (1 - \cos 2x)\,dx)(= \frac{1}{2} \left( \int 1\,dx - \int \cos 2x\,dx \right))(= \frac{1}{2} \left( x - \frac{\sin 2x}{2} \right) + C)(= \frac{1}{2}x - \frac{\sin 2x}{4} + C).