Question

Using \(\cos^2 x = \frac{1+\cos 2x}{2}\), which expression is equivalent to \(\int \cos^2 x\,dx\)?

Options

• \(\frac{1}{2}\int(1+\cos 2x)\,dx\)

• \(\int(1+\cos 2x)\,dx\)

• \(2\int(1+\cos 2x)\,dx\)

• \(\frac{1}{2}\int(1-\cos 2x)\,dx\)

Answer 1

Substituting \(\cos^2 x = \frac{1+\cos 2x}{2}\) places the factor \(\frac{1}{2}\) outside the integral. Thus, the integral becomes \(\frac{1}{2}\int(1+\cos 2x)\,dx\).