What is the integral from 0 to 3pi of 1+cos(x) ?

The integral from 0 to 3pi of 1+cos(x) is 3pi

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integral from 0 to 3pi of 1+cos(x)

\int_{0}^{3 π} 1 + cos (x) d x

3 π

Decimal Notation

9.42477 \dots

Solution steps

\int_{0}^{3 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}^{3 π} 1 d x + \int_{0}^{3 π} cos (x) d x

\int_{0}^{3 π} 1 d x = 3 π

\int_{0}^{3 π} cos (x) d x = 0

= 3 π + 0

Simplify

= 3 π

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What is the integral from 0 to 3pi of 1+cos(x) ?
The integral from 0 to 3pi of 1+cos(x) is 3pi