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

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

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

\int_{0}^{2 π} cos (x) + 1 d x

2 π

Decimal

6.28318 \dots

Solution steps

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

\int_{0}^{2 π} cos (x) d x = 0

\int_{0}^{2 π} 1 d x = 2 π

= 0 + 2 π

Simplify

= 2 π

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\int_{0}^{12} 144 - x^{2} d x

\int_{0}^{5} \frac{1}{25 + t ^{2}} d t

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