What is the integral from 0 to 2pi of cos^2(y) ?

The integral from 0 to 2pi of cos^2(y) is pi

Popular >

integral from 0 to 2pi of cos^2(y)

\int_{0}^{2 π} cos^{2} (y) d y

π

Solution steps

\int_{0}^{2 π} cos^{2} (y) d y

Rewrite using trig identities

= \int_{0}^{2 π} \frac{1 + cos ( 2 y )}{2} d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{0}^{2 π} 1 + cos (2 y) d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int_{0}^{2 π} 1 d y + \int_{0}^{2 π} cos (2 y) d y)

\int_{0}^{2 π} 1 d y = 2 π

\int_{0}^{2 π} cos (2 y) d y = 0

= \frac{1}{2} (2 π + 0)

Simplify

\frac{1}{2} (2 π + 0) : π

= π

\int_{1}^{9} \frac{4}{x} d x

\int_{1}^{6} \frac{4}{x ^{2}} d x

\int_{2}^{e} \frac{x ^{4} - 3 x}{x ^{2}} d x

\int_{- 1}^{1} x^{3} sin (x) d x

\int_{1}^{4} \frac{∣ 2 - x ∣}{x} d x

What is the integral from 0 to 2pi of cos^2(y) ?
The integral from 0 to 2pi of cos^2(y) is pi