What is the integral from 0 to pi/2 of (8+4cos(x)) ?

The integral from 0 to pi/2 of (8+4cos(x)) is 4pi+4

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integral from 0 to pi/2 of (8+4cos(x))

\int_{0}^{\frac{π}{2}} (8 + 4 cos (x)) d x

4 π + 4

Decimal

16.56637 \dots

Solution steps

\int_{0}^{\frac{π}{2}} 8 + 4 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}^{\frac{π}{2}} 8 d x + \int_{0}^{\frac{π}{2}} 4 cos (x) d x

\int_{0}^{\frac{π}{2}} 8 d x = 4 π

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

= 4 π + 4

What is the integral from 0 to pi/2 of (8+4cos(x)) ?
The integral from 0 to pi/2 of (8+4cos(x)) is 4pi+4