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

The integral from 0 to pi of 3e^xsin(x) is (3e^pi+3)/2

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

\int_{0}^{π} 3 e^{x} sin (x) d x

\frac{3 e ^{π} + 3}{2}

Decimal

36.21103 \dots

Solution steps

\int_{0}^{π} 3 e^{x} sin (x) d x

Compute the indefinite integral:

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

Compute the boundaries:

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

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

Simplify

= \frac{3 e ^{π} + 3}{2}

\frac{d}{d x} (\frac{1}{9 - x ^{2}})

\frac{1}{( s + 1 ) ^{2} \cdot ( s - 1 )}

h \to 0 lim (\frac{8 ^{h} - 1}{h})

f (x) = \frac{x ^{2} + 2 x - 3}{( x + 1 ) ^{2}}

\int_{- \infty}^{0} \frac{1}{6 - 4 x} d x

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