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 Notation

- 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}

\frac{\partial}{\partial x} (x^{2} + 3 y^{3})

\int \frac{100}{w ^{2} 25 - w ^{2}} d w

x y^{^{'}} - 2 y = 3 x^{2}

f (x) = 1 - 6 x, at x = - 1

\frac{9 x}{x}

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