What is the integral from 0 to pi of cos(x)cos(x) ?

The integral from 0 to pi of cos(x)cos(x) is pi/2

Popular >

integral from 0 to pi of cos(x)cos(x)

\int_{0}^{π} cos (x) cos (x) d x

\frac{π}{2}

Decimal

1.57079 \dots

Solution steps

\int_{0}^{π} cos (x) cos (x) d x

Simplify

cos (x) cos (x) : cos^{2} (x)

= \int_{0}^{π} cos^{2} (x) d x

Rewrite using trig identities

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

Take the constant out:

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

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

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

\int_{0}^{π} 1 d x = π

\int_{0}^{π} cos (2 x) d x = 0

= \frac{1}{2} (π + 0)

Simplify

\frac{1}{2} (π + 0) : \frac{π}{2}

= \frac{π}{2}

\int_{- 2}^{2} x^{2} - 4 x d x

\int_{0}^{s i n (θ)} sec^{2} (y) d y

\int_{- 2}^{\infty} e^{- 3 x} d x

\int_{0}^{\frac{4}{11}} \frac{1}{121 x ^{2} + 16} d x

\int_{1}^{3} \frac{x ^{3} - 1}{x ^{2} - 1} d x

What is the integral from 0 to pi of cos(x)cos(x) ?
The integral from 0 to pi of cos(x)cos(x) is pi/2