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

The integral from 0 to pi of e^xsin(x) is (e^pi+1)/2

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

\int_{0}^{π} e^{x} sin (x) d x

\frac{e ^{π} + 1}{2}

Decimal Notation

12.07034 \dots

Solution steps

\int_{0}^{π} e^{x} sin (x) d x

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{π} e^{x} sin (x) d x = \frac{e ^{π}}{2} - (- \frac{1}{2})

= \frac{e ^{π}}{2} - (- \frac{1}{2})

Simplify

= \frac{e ^{π} + 1}{2}

x \to + 0 lim (\frac{sin ( x )}{4 x})

1500 x + 3000 (4 x + 3)^{- 1} - 1000

\frac{d}{d x} (f (x^{2})) = x^{4}

\frac{d ^{2} y}{d θ ^{2}} + y = 0

\int (x^{2} - 2) (x^{3} - 6 x)^{207} d x

What is the integral from 0 to pi of e^xsin(x) ?
The integral from 0 to pi of e^xsin(x) is (e^pi+1)/2