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

The integral from 0 to 2pi of 2-2cos(x) is 4pi

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

\int_{0}^{2 π} 2 - 2 cos (x) d x

4 π

Decimal

12.56637 \dots

Solution steps

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

\int_{0}^{2 π} 2 d x = 4 π

\int_{0}^{2 π} 2 cos (x) d x = 0

= 4 π - 0

Simplify

= 4 π

What is the integral from 0 to 2pi of 2-2cos(x) ?
The integral from 0 to 2pi of 2-2cos(x) is 4pi