What is the integral from 0 to pi of 4e^x+7sin(x) ?

The integral from 0 to pi of 4e^x+7sin(x) is 4e^pi+10

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integral from 0 to pi of 4e^x+7sin(x)

\int_{0}^{π} 4 e^{x} + 7 sin (x) d x

4 e^{π} + 10

Decimal

102.56277 \dots

Solution steps

\int_{0}^{π} 4 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} 4 e^{x} d x + \int_{0}^{π} 7 sin (x) d x

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

\int_{0}^{π} 7 sin (x) d x = 14

= 4 (e^{π} - 1) + 14

Simplify

4 (e^{π} - 1) + 14 : 4 e^{π} + 10

= 4 e^{π} + 10

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What is the integral from 0 to pi of 4e^x+7sin(x) ?
The integral from 0 to pi of 4e^x+7sin(x) is 4e^pi+10