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

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

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

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

\frac{π}{4} + 1

Decimal

1.78539 \dots

Solution steps

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

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

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

= \frac{π}{4} + 1

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