What is the integral from 0 to 10 of e^xsin(x) ?

The integral from 0 to 10 of e^xsin(x) is (-e^{10}cos(10)+e^{10}sin(10)+1)/2

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integral from 0 to 10 of e^xsin(x)

\int_{0}^{10} e^{x} sin (x) d x

\frac{- e ^{10} cos ( 10 ) + e ^{10} sin ( 10 ) + 1}{2}

Decimal Notation

3249.95897 \dots

Solution steps

\int_{0}^{10} 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}^{10} e^{x} sin (x) d x = \frac{- e ^{10} cos ( 10 ) + e ^{10} sin ( 10 )}{2} - (- \frac{1}{2})

= \frac{- e ^{10} cos ( 10 ) + e ^{10} sin ( 10 )}{2} - (- \frac{1}{2})

Simplify

= \frac{- e ^{10} cos ( 10 ) + e ^{10} sin ( 10 ) + 1}{2}

\frac{d}{d x} ((\frac{x ^{2} + 1}{x ^{2} - 1})^{6})

x \to 3 - lim (x^{2})

\int_{0}^{1} \frac{x ^{3} + 4}{x ^{2} - 25} d x

y = \frac{9 x}{x}

\int t \cdot cos (n t) d t

What is the integral from 0 to 10 of e^xsin(x) ?
The integral from 0 to 10 of e^xsin(x) is (-e^{10}cos(10)+e^{10}sin(10)+1)/2