What is the integral from 0 to pi of (1-cos(θ))^2 ?

The integral from 0 to pi of (1-cos(θ))^2 is pi+pi/2

Popular >

integral from 0 to pi of (1-cos(θ))^2

\int_{0}^{π} (1 - cos (θ))^{2} d θ

π + \frac{π}{2}

Decimal Notation

4.71238 \dots

Solution steps

\int_{0}^{π} (1 - cos (θ))^{2} d θ

Expand

(1 - cos (θ))^{2} : 1 - 2 cos (θ) + cos^{2} (θ)

= \int_{0}^{π} 1 - 2 cos (θ) + cos^{2} (θ) d θ

Apply the Sum Rule:

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

= \int_{0}^{π} 1 d θ - \int_{0}^{π} 2 cos (θ) d θ + \int_{0}^{π} cos^{2} (θ) d θ

\int_{0}^{π} 1 d θ = π

\int_{0}^{π} 2 cos (θ) d θ = 0

\int_{0}^{π} cos^{2} (θ) d θ = \frac{π}{2}

= π - 0 + \frac{π}{2}

Simplify

= π + \frac{π}{2}

\int_{0}^{1} 3^{x^{3}} d x

\int_{0}^{\infty} x^{8} e^{- x} d x

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

\int_{0}^{\frac{π}{6}} \frac{1}{cos ^{2} ( 4 x )} d x

\int_{0}^{1} 16 - 9 x^{2} d x

What is the integral from 0 to pi of (1-cos(θ))^2 ?
The integral from 0 to pi of (1-cos(θ))^2 is pi+pi/2