What is the integral from 0 to 4 of e^xsin(x) ?

The integral from 0 to 4 of e^xsin(x) is (-e^4cos(4)+e^4sin(4)+1)/2

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integral from 0 to 4 of e^xsin(x)

\int_{0}^{4} e^{x} sin (x) d x

\frac{- e ^{4} cos ( 4 ) + e ^{4} sin ( 4 ) + 1}{2}

Decimal

- 2.31614 \dots

Solution steps

\int_{0}^{4} 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}^{4} e^{x} sin (x) d x = \frac{- e ^{4} cos ( 4 ) + e ^{4} sin ( 4 )}{2} - (- \frac{1}{2})

= \frac{- e ^{4} cos ( 4 ) + e ^{4} sin ( 4 )}{2} - (- \frac{1}{2})

Simplify

= \frac{- e ^{4} cos ( 4 ) + e ^{4} sin ( 4 ) + 1}{2}

What is the integral from 0 to 4 of e^xsin(x) ?
The integral from 0 to 4 of e^xsin(x) is (-e^4cos(4)+e^4sin(4)+1)/2