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

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

Popular >

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

\int_{0}^{2 π} cos^{2} (u) d u

π

Decimal

3.14159 \dots

Solution steps

\int_{0}^{2 π} cos^{2} (u) d u

Rewrite using trig identities

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

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 u) d u

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 u + \int_{0}^{2 π} cos (2 u) d u)

\int_{0}^{2 π} 1 d u = 2 π

\int_{0}^{2 π} cos (2 u) d u = 0

= \frac{1}{2} (2 π + 0)

Simplify

\frac{1}{2} (2 π + 0) : π

= π

\int_{2}^{4} x ln (x) d x

\int_{0}^{4} x y d x

\int_{0}^{1} ln (x + 2) d x

\int_{2}^{4} \frac{2 x ^{2}}{x + 2} d x

\int_{7}^{13} 4 x^{5} d x

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