What is the integral from 0 to 9 of e^xsin(x) ?

The integral from 0 to 9 of e^xsin(x) is (-e^9cos(9)+e^9sin(9)+1)/2

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integral from 0 to 9 of e^xsin(x)

\int_{0}^{9} e^{x} sin (x) d x

\frac{- e ^{9} cos ( 9 ) + e ^{9} sin ( 9 ) + 1}{2}

Decimal Notation

5361.69782 \dots

Solution steps

\int_{0}^{9} 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}^{9} e^{x} sin (x) d x = \frac{- e ^{9} cos ( 9 ) + e ^{9} sin ( 9 )}{2} - (- \frac{1}{2})

= \frac{- e ^{9} cos ( 9 ) + e ^{9} sin ( 9 )}{2} - (- \frac{1}{2})

Simplify

= \frac{- e ^{9} cos ( 9 ) + e ^{9} sin ( 9 ) + 1}{2}

\int_{0}^{x} 3 t + 5 d t

e^{- t} + e^{t}

y^{^{''}} + 4 y^{^{'}} + 5 y = 5 x + 3 e^{- x}

2 t \frac{d y}{d t} + y = t^{4}

x \to - 2 - lim (4 x^{2} - 7)

What is the integral from 0 to 9 of e^xsin(x) ?
The integral from 0 to 9 of e^xsin(x) is (-e^9cos(9)+e^9sin(9)+1)/2