What is the integral from 0 to pi of (3e^x+8sin(x)) ?

The integral from 0 to pi of (3e^x+8sin(x)) is 3e^pi+13

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integral from 0 to pi of (3e^x+8sin(x))

\int_{0}^{π} (3 e^{x} + 8 sin (x)) d x

3 e^{π} + 13

Decimal

82.42207 \dots

Solution steps

\int_{0}^{π} 3 e^{x} + 8 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} 3 e^{x} d x + \int_{0}^{π} 8 sin (x) d x

\int_{0}^{π} 3 e^{x} d x = 3 (e^{π} - 1)

\int_{0}^{π} 8 sin (x) d x = 16

= 3 (e^{π} - 1) + 16

Simplify

3 (e^{π} - 1) + 16 : 3 e^{π} + 13

= 3 e^{π} + 13

What is the integral from 0 to pi of (3e^x+8sin(x)) ?
The integral from 0 to pi of (3e^x+8sin(x)) is 3e^pi+13