What is the integral from 0 to pi of (9e^x+6sin(x)) ?

The integral from 0 to pi of (9e^x+6sin(x)) is 9e^pi+3

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integral from 0 to pi of (9e^x+6sin(x))

\int_{0}^{π} (9 e^{x} + 6 sin (x)) d x

9 e^{π} + 3

Decimal

211.26623 \dots

Solution steps

\int_{0}^{π} 9 e^{x} + 6 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} 9 e^{x} d x + \int_{0}^{π} 6 sin (x) d x

\int_{0}^{π} 9 e^{x} d x = 9 (e^{π} - 1)

\int_{0}^{π} 6 sin (x) d x = 12

= 9 (e^{π} - 1) + 12

Simplify

9 (e^{π} - 1) + 12 : 9 e^{π} + 3

= 9 e^{π} + 3

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What is the integral from 0 to pi of (9e^x+6sin(x)) ?
The integral from 0 to pi of (9e^x+6sin(x)) is 9e^pi+3