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

The integral from 0 to pi of 7e^xsin(x) is (7e^pi+7)/2

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integral from 0 to pi of 7e^xsin(x)

\int_{0}^{π} 7 e^{x} sin (x) d x

\frac{7 e ^{π} + 7}{2}

Decimal Notation

84.49242 \dots

Solution steps

\int_{0}^{π} 7 e^{x} sin (x) d x

Compute the indefinite integral:

\int 7 e^{x} sin (x) d x = 7 (- \frac{e ^{x} cos ( x )}{2} + \frac{e ^{x} sin ( x )}{2}) + C

Compute the boundaries:

\int_{0}^{π} 7 e^{x} sin (x) d x = 7 \cdot \frac{e ^{π}}{2} - (- \frac{7}{2})

= 7 \cdot \frac{e ^{π}}{2} - (- \frac{7}{2})

Simplify

= \frac{7 e ^{π} + 7}{2}

f (x) = \frac{1}{3 + 2 x}, at x = 2

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What is the integral from 0 to pi of 7e^xsin(x) ?
The integral from 0 to pi of 7e^xsin(x) is (7e^pi+7)/2