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

The integral from 0 to 2pi of 1-cos(x) is 2pi

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integral from 0 to 2pi of 1-cos(x)

\int_{0}^{2 π} 1 - cos (x) d x

2 π

Decimal

6.28318 \dots

Solution steps

\int_{0}^{2 π} 1 - cos (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

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

\int_{0}^{2 π} 1 d x = 2 π

\int_{0}^{2 π} cos (x) d x = 0

= 2 π - 0

Simplify

= 2 π

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

\int_{0}^{\frac{1}{2}} x e^{3 x} d x

\int_{0}^{y} x^{2} e^{- x y} d x

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