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

The integral from 0 to pi of 5e^xsin(x) is (5e^pi+5)/2

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integral from 0 to pi of 5e^xsin(x)

\int_{0}^{π} 5 e^{x} sin (x) d x

\frac{5 e ^{π} + 5}{2}

Decimal

60.35173 \dots

Solution steps

\int_{0}^{π} 5 e^{x} sin (x) d x

Compute the indefinite integral:

\int 5 e^{x} sin (x) d x = 5 (- \frac{e ^{x} cos ( x )}{2} + \frac{e ^{x} sin ( x )}{2}) + C

Compute the boundaries:

\int_{0}^{π} 5 e^{x} sin (x) d x = 5 \cdot \frac{e ^{π}}{2} - (- \frac{5}{2})

= 5 \cdot \frac{e ^{π}}{2} - (- \frac{5}{2})

Simplify

= \frac{5 e ^{π} + 5}{2}

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What is the integral from 0 to pi of 5e^xsin(x) ?
The integral from 0 to pi of 5e^xsin(x) is (5e^pi+5)/2