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Calculadora de integrales definidas e impropias
Calcular integrales definidas e impropias paso a paso
La calculadora intentará evaluar la integral definida (es decir, con límites de integración), incluyendo las impropias, mostrando los pasos.
Solution
Your input: calculate $$$\int_{0}^{1}\left( x^{2} e^{x} \right)dx$$$
First, calculate the corresponding indefinite integral: $$$\int{x^{2} e^{x} d x}=\left(x^{2} - 2 x + 2\right) e^{x}$$$ (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.
$$$\left(\left(x^{2} - 2 x + 2\right) e^{x}\right)|_{\left(x=1\right)}=e$$$
$$$\left(\left(x^{2} - 2 x + 2\right) e^{x}\right)|_{\left(x=0\right)}=2$$$
$$$\int_{0}^{1}\left( x^{2} e^{x} \right)dx=\left(\left(x^{2} - 2 x + 2\right) e^{x}\right)|_{\left(x=1\right)}-\left(\left(x^{2} - 2 x + 2\right) e^{x}\right)|_{\left(x=0\right)}=-2 + e$$$
Answer: $$$\int_{0}^{1}\left( x^{2} e^{x} \right)dx=-2 + e\approx 0.718281828459045$$$