What is the integral from-infinity to 0 of sin(x)e^x ?

The integral from-infinity to 0 of sin(x)e^x is -1/2

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integral from-infinity to 0 of sin(x)e^x

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

- \frac{1}{2}

Decimal

- 0.5

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= - \frac{1}{2} - 0

Simplify

= - \frac{1}{2}

\int_{- x}^{x} t^{3} + t d t

\int_{3}^{6} (- 5 x + 6) d x

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

\int_{0}^{c} 2 e^{x} d x

\int_{1}^{e^{3}} \frac{2}{x} d x

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