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

The integral from 0 to 7 of e^xsin(x) is (-e^7cos(7)+e^7sin(7)+1)/2

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

\int_{0}^{7} e^{x} sin (x) d x

\frac{- e ^{7} cos ( 7 ) + e ^{7} sin ( 7 ) + 1}{2}

Decimal Notation

- 52.64046 \dots

Solution steps

\int_{0}^{7} 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}^{7} e^{x} sin (x) d x = \frac{- e ^{7} cos ( 7 ) + e ^{7} sin ( 7 )}{2} - (- \frac{1}{2})

= \frac{- e ^{7} cos ( 7 ) + e ^{7} sin ( 7 )}{2} - (- \frac{1}{2})

Simplify

= \frac{- e ^{7} cos ( 7 ) + e ^{7} sin ( 7 ) + 1}{2}

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What is the integral from 0 to 7 of e^xsin(x) ?
The integral from 0 to 7 of e^xsin(x) is (-e^7cos(7)+e^7sin(7)+1)/2