What is the integral from 0 to 2 of e^xsin(x) ?

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

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integral from 0 to 2 of e^xsin(x)

\int_{0}^{2} e^{x} sin (x) d x

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

Decimal

5.39689 \dots

Solution steps

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

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

Simplify

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

y^{^{''}} - 2 y^{^{'}} + y = 2 cos (t) + 4 sin (t), y (0) = 3, y^{^{'}} (0) = 2

\frac{1}{14 x ^{2}}, x, \frac{x}{8}

\frac{\partial}{\partial x} (e^{- x^{4} - y^{5}})

\frac{d}{d x} (- \frac{1}{2 sin ^{2} ( x )})

\int \frac{2 ^{x} \cdot 3 ^{x}}{9 ^{x} - 4 ^{x}} d x

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