What is the integral from 0 to 3 of e^xsin(x) ?

The integral from 0 to 3 of e^xsin(x) is (-e^3cos(3)+e^3sin(3)+1)/2

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integral from 0 to 3 of e^xsin(x)

\int_{0}^{3} e^{x} sin (x) d x

\frac{- e ^{3} cos ( 3 ) + e ^{3} sin ( 3 ) + 1}{2}

Decimal

11.85950 \dots

Solution steps

\int_{0}^{3} 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}^{3} e^{x} sin (x) d x = \frac{- e ^{3} cos ( 3 ) + e ^{3} sin ( 3 )}{2} - (- \frac{1}{2})

= \frac{- e ^{3} cos ( 3 ) + e ^{3} sin ( 3 )}{2} - (- \frac{1}{2})

Simplify

= \frac{- e ^{3} cos ( 3 ) + e ^{3} sin ( 3 ) + 1}{2}

h \to 0 lim (\frac{1}{h + 1})

\int x^{- 3} (x + 1) d x

\int_{0}^{1} 8^{2 x} d x

d er i v a t i v e 5 x sin (x^{2})

\int \frac{e ^{x}}{x} d x

What is the integral from 0 to 3 of e^xsin(x) ?
The integral from 0 to 3 of e^xsin(x) is (-e^3cos(3)+e^3sin(3)+1)/2