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_{4}^{x} \frac{64}{t ^{5}} d t

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