|
|
|
|
|
|
|
|
|
|
|
|
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 $$$\int_{11}^{12}\left( x^{2} \right)dx$$$
First, calculate the corresponding indefinite integral: $$$\int{x^{2} d x}=\frac{x^{3}}{3}$$$ (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.
$$$\left(\frac{x^{3}}{3}\right)|_{\left(x=12\right)}=576$$$
$$$\left(\frac{x^{3}}{3}\right)|_{\left(x=11\right)}=\frac{1331}{3}$$$
$$$\int_{11}^{12}\left( x^{2} \right)dx=\left(\frac{x^{3}}{3}\right)|_{\left(x=12\right)}-\left(\frac{x^{3}}{3}\right)|_{\left(x=11\right)}=\frac{397}{3}$$$
Answer: $$$\int_{11}^{12}\left( x^{2} \right)dx=\frac{397}{3}\approx 132.333333333333$$$