What is the integral from 0 to pi of (5e^x+7sin(x)) ?

The integral from 0 to pi of (5e^x+7sin(x)) is 5e^pi+9

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integral from 0 to pi of (5e^x+7sin(x))

\int_{0}^{π} (5 e^{x} + 7 sin (x)) d x

5 e^{π} + 9

Decimal

124.70346 \dots

Solution steps

\int_{0}^{π} 5 e^{x} + 7 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} 5 e^{x} d x + \int_{0}^{π} 7 sin (x) d x

\int_{0}^{π} 5 e^{x} d x = 5 (e^{π} - 1)

\int_{0}^{π} 7 sin (x) d x = 14

= 5 (e^{π} - 1) + 14

Simplify

5 (e^{π} - 1) + 14 : 5 e^{π} + 9

= 5 e^{π} + 9

What is the integral from 0 to pi of (5e^x+7sin(x)) ?
The integral from 0 to pi of (5e^x+7sin(x)) is 5e^pi+9