What is the integral from 0 to 2 of e^{2x}sin(3x) ?

The integral from 0 to 2 of e^{2x}sin(3x) is (-3e^4cos(6)+2e^4sin(6)+3)/(13)

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integral from 0 to 2 of e^{2x}sin(3x)

\int_{0}^{2} e^{2 x} sin (3 x) d x

\frac{- 3 e ^{4} cos ( 6 ) + 2 e ^{4} sin ( 6 ) + 3}{13}

Decimal Notation

- 14.21397 \dots

Solution steps

\int_{0}^{2} e^{2 x} sin (3 x) d x

Compute the indefinite integral:

\int e^{2 x} sin (3 x) d x = - \frac{3 e ^{2 x} cos ( 3 x )}{13} + \frac{2 e ^{2 x} sin ( 3 x )}{13} + C

Compute the boundaries:

\int_{0}^{2} e^{2 x} sin (3 x) d x = \frac{- 3 e ^{4} cos ( 6 ) + 2 e ^{4} sin ( 6 )}{13} - (- \frac{3}{13})

= \frac{- 3 e ^{4} cos ( 6 ) + 2 e ^{4} sin ( 6 )}{13} - (- \frac{3}{13})

Simplify

= \frac{- 3 e ^{4} cos ( 6 ) + 2 e ^{4} sin ( 6 ) + 3}{13}

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What is the integral from 0 to 2 of e^{2x}sin(3x) ?
The integral from 0 to 2 of e^{2x}sin(3x) is (-3e^4cos(6)+2e^4sin(6)+3)/(13)