What is the integral from 0 to 4pi of 6+2cos(1/2 x) ?

The integral from 0 to 4pi of 6+2cos(1/2 x) is 24pi

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integral from 0 to 4pi of 6+2cos(1/2 x)

\int_{0}^{4 π} 6 + 2 cos (\frac{1}{2} x) d x

24 π

Decimal

75.39822 \dots

Solution steps

\int_{0}^{4 π} 6 + 2 cos (\frac{1}{2} 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}^{4 π} 6 d x + \int_{0}^{4 π} 2 cos (\frac{1}{2} x) d x

\int_{0}^{4 π} 6 d x = 24 π

\int_{0}^{4 π} 2 cos (\frac{1}{2} x) d x = 0

= 24 π + 0

Simplify

= 24 π

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What is the integral from 0 to 4pi of 6+2cos(1/2 x) ?
The integral from 0 to 4pi of 6+2cos(1/2 x) is 24pi