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}-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}} - 2

Decimal

2.81047 \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}} - 2

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\int_{1}^{3} 4 e^{2 x - 5} d x

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}-2