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

The integral from 0 to pi of 9e^xsin(x) is (9e^pi+9)/2

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integral from 0 to pi of 9e^xsin(x)

\int_{0}^{π} 9 e^{x} sin (x) d x

\frac{9 e ^{π} + 9}{2}

Decimal Notation

108.63311 \dots

Solution steps

\int_{0}^{π} 9 e^{x} sin (x) d x

Compute the indefinite integral:

\int 9 e^{x} sin (x) d x = 9 (- \frac{e ^{x} cos ( x )}{2} + \frac{e ^{x} sin ( x )}{2}) + C

Compute the boundaries:

\int_{0}^{π} 9 e^{x} sin (x) d x = 9 \cdot \frac{e ^{π}}{2} - (- \frac{9}{2})

= 9 \cdot \frac{e ^{π}}{2} - (- \frac{9}{2})

Simplify

= \frac{9 e ^{π} + 9}{2}

\frac{d}{d x} (arctan (sec (x) + tan (x)))

y = \frac{sin ( x )}{x ^{2}}

\frac{d}{d x} (\frac{5}{x + 1})

y^{^{'}} x y = x^{2} + 2 y^{2}

\frac{d}{d x} ((\frac{1 - 2 x}{1 + 3 x})^{4})

What is the integral from 0 to pi of 9e^xsin(x) ?
The integral from 0 to pi of 9e^xsin(x) is (9e^pi+9)/2