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

The integral from 0 to pi/2 of (e^x+cos(x)) is e^{pi/2}

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

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

e^{\frac{π}{2}}

Decimal

4.81047 \dots

Solution steps

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

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

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

= e^{\frac{π}{2}} - 1 + 1

Simplify

= e^{\frac{π}{2}}

What is the integral from 0 to pi/2 of (e^x+cos(x)) ?
The integral from 0 to pi/2 of (e^x+cos(x)) is e^{pi/2}