What is the integral from 0 to 8 of e^xsin(x) ?

The integral from 0 to 8 of e^xsin(x) is (-e^8cos(8)+e^8sin(8)+1)/2

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integral from 0 to 8 of e^xsin(x)

\int_{0}^{8} e^{x} sin (x) d x

\frac{- e ^{8} cos ( 8 ) + e ^{8} sin ( 8 ) + 1}{2}

Decimal

1691.98242 \dots

Solution steps

\int_{0}^{8} 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}^{8} e^{x} sin (x) d x = \frac{- e ^{8} cos ( 8 ) + e ^{8} sin ( 8 )}{2} - (- \frac{1}{2})

= \frac{- e ^{8} cos ( 8 ) + e ^{8} sin ( 8 )}{2} - (- \frac{1}{2})

Simplify

= \frac{- e ^{8} cos ( 8 ) + e ^{8} sin ( 8 ) + 1}{2}

What is the integral from 0 to 8 of e^xsin(x) ?
The integral from 0 to 8 of e^xsin(x) is (-e^8cos(8)+e^8sin(8)+1)/2