Calculadora de Integrais Definidas e Impróprias
Calcule integrais definidas e impróprias passo a passo
A calculadora tentará calcular a integral definida (isto é, com limites), inclusive no caso impróprio, com os passos mostrados.
Solution
Your input: calculate $$$\int_{e^{-1}}^{0}\left( x \right)dx$$$
First, calculate the corresponding indefinite integral: $$$\int{x d x}=\frac{x^{2}}{2}$$$ (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.
$$$\left(\frac{x^{2}}{2}\right)|_{\left(x=0\right)}=0$$$
$$$\left(\frac{x^{2}}{2}\right)|_{\left(x=e^{-1}\right)}=\frac{1}{2 e^{2}}$$$
$$$\int_{e^{-1}}^{0}\left( x \right)dx=\left(\frac{x^{2}}{2}\right)|_{\left(x=0\right)}-\left(\frac{x^{2}}{2}\right)|_{\left(x=e^{-1}\right)}=- \frac{1}{2 e^{2}}$$$
Answer: $$$\int_{e^{-1}}^{0}\left( x \right)dx=- \frac{1}{2 e^{2}}\approx -0.0676676416183064$$$