Question

Evaluate the integral of cos² y dy.

Answer 1

cos²(y) = \(\frac{1+cos(2y)}{2}\)

\(\int cos^2(y) dy = \int \frac{1+cos(2y)}{2} dy\)

\(\int \frac{1}{2} dy + \int\frac{cos(2y)}{2} dy\)

\(\int \frac{1}{2} dy = \frac{y}{2}\)

\(\int cos(2y) dy = \frac{sin(2y)}{2}\)

\(\frac{y}{2} + \frac{sin(2y)}{4} + C\)

where C is the constant of integration.