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

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

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

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

8 e^{π} + 8

Decimal

193.12554 \dots

Solution steps

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

\int_{0}^{π} 8 e^{x} d x = 8 (e^{π} - 1)

\int_{0}^{π} 8 sin (x) d x = 16

= 8 (e^{π} - 1) + 16

Simplify

8 (e^{π} - 1) + 16 : 8 e^{π} + 8

= 8 e^{π} + 8

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