What is the integral from 0 to pi/4 of e^{3x}sin(2x) ?

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

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integral from 0 to pi/4 of e^{3x}sin(2x)

\int_{0}^{\frac{π}{4}} e^{3 x} sin (2 x) d x

\frac{3 e ^{\frac{3 π}{4}} + 2}{13}

Decimal Notation

2.58862 \dots

Solution steps

\int_{0}^{\frac{π}{4}} e^{3 x} sin (2 x) d x

Compute the indefinite integral:

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

Compute the boundaries:

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

= \frac{3 e ^{\frac{3 π}{4}}}{13} - (- \frac{2}{13})

Simplify

= \frac{3 e ^{\frac{3 π}{4}} + 2}{13}

\int_{0}^{b} x e^{- a x} d x

\int_{1}^{5} \frac{x}{12} d x

\int_{1}^{2} \frac{x}{6} d x

\int_{- 2}^{2} t d t

\int_{- 1}^{1} x \cdot e^{x} d x

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