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 $$$\int_{11}^{12}\left( 2 x \right)dx$$$
First, calculate the corresponding indefinite integral: $$$\int{2 x d x}=x^{2}$$$ (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.
$$$\left(x^{2}\right)|_{\left(x=12\right)}=144$$$
$$$\left(x^{2}\right)|_{\left(x=11\right)}=121$$$
$$$\int_{11}^{12}\left( 2 x \right)dx=\left(x^{2}\right)|_{\left(x=12\right)}-\left(x^{2}\right)|_{\left(x=11\right)}=23$$$
Answer: $$$\int_{11}^{12}\left( 2 x \right)dx=23$$$