What is the integral from 0 to pi of (4e^x+9sin(x)) ?

The integral from 0 to pi of (4e^x+9sin(x)) is 4e^pi+14

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integral from 0 to pi of (4e^x+9sin(x))

\int_{0}^{π} (4 e^{x} + 9 sin (x)) d x

4 e^{π} + 14

Decimal

106.56277 \dots

Solution steps

\int_{0}^{π} 4 e^{x} + 9 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} 4 e^{x} d x + \int_{0}^{π} 9 sin (x) d x

\int_{0}^{π} 4 e^{x} d x = 4 (e^{π} - 1)

\int_{0}^{π} 9 sin (x) d x = 18

= 4 (e^{π} - 1) + 18

Simplify

4 (e^{π} - 1) + 18 : 4 e^{π} + 14

= 4 e^{π} + 14

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What is the integral from 0 to pi of (4e^x+9sin(x)) ?
The integral from 0 to pi of (4e^x+9sin(x)) is 4e^pi+14