Calculadora de integrales definidas e impropias

La calculadora intentará evaluar la integral definida (es decir, con límites de integración), incluyendo las impropias, mostrando los pasos.

Enter a function:

Integrate with respect to:

Enter a lower limit:

If you need `-oo`, type -inf.

Enter an upper limit:

If you need `oo`, type inf.

Please write without any differentials such as `dx`, `dy` etc.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

Solution

Your input: calculate $$$\int_{0}^{2}\left( x e^{- x} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{x e^{- x} d x}=\left(- x - 1\right) e^{- x}$$$ (for steps, see indefinite integral calculator)

According to the Fundamental Theorem of Calculus, $$$\int_a^b F(x) dx=f(b)-f(a)$$$, so just evaluate the integral at the endpoints, and that's the answer.

$$$\left(\left(- x - 1\right) e^{- x}\right)|_{\left(x=2\right)}=- \frac{3}{e^{2}}$$$

$$$\left(\left(- x - 1\right) e^{- x}\right)|_{\left(x=0\right)}=-1$$$

$$$\int_{0}^{2}\left( x e^{- x} \right)dx=\left(\left(- x - 1\right) e^{- x}\right)|_{\left(x=2\right)}-\left(\left(- x - 1\right) e^{- x}\right)|_{\left(x=0\right)}=1 - \frac{3}{e^{2}}$$$

Answer: $$$\int_{0}^{2}\left( x e^{- x} \right)dx=1 - \frac{3}{e^{2}}\approx 0.593994150290162$$$

Please try a new game Rotatly

Calculadora de integrales definidas e impropias

Calcular integrales definidas e impropias paso a paso

Solution