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 $$$\int_{0}^{2}\left( e^{2 x} \right)dx$$$
First, calculate the corresponding indefinite integral: $$$\int{e^{2 x} d x}=\frac{e^{2 x}}{2}$$$ (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.
$$$\left(\frac{e^{2 x}}{2}\right)|_{\left(x=2\right)}=\frac{e^{4}}{2}$$$
$$$\left(\frac{e^{2 x}}{2}\right)|_{\left(x=0\right)}=\frac{1}{2}$$$
$$$\int_{0}^{2}\left( e^{2 x} \right)dx=\left(\frac{e^{2 x}}{2}\right)|_{\left(x=2\right)}-\left(\frac{e^{2 x}}{2}\right)|_{\left(x=0\right)}=- \frac{1}{2} + \frac{e^{4}}{2}$$$
Answer: $$$\int_{0}^{2}\left( e^{2 x} \right)dx=- \frac{1}{2} + \frac{e^{4}}{2}\approx 26.7990750165721$$$