What is the integral from 0 to pi of e^x-sin(x) ?

The integral from 0 to pi of e^x-sin(x) is e^pi-3

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integral from 0 to pi of e^x-sin(x)

\int_{0}^{π} e^{x} - sin (x) d x

e^{π} - 3

Decimal

20.14069 \dots

Solution steps

\int_{0}^{π} e^{x} - sin (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}^{π} e^{x} d x - \int_{0}^{π} sin (x) d x

\int_{0}^{π} e^{x} d x = e^{π} - 1

\int_{0}^{π} sin (x) d x = 2

= e^{π} - 1 - 2

Simplify

= e^{π} - 3

What is the integral from 0 to pi of e^x-sin(x) ?
The integral from 0 to pi of e^x-sin(x) is e^pi-3