|
|
|
|
|
|
|
|
|
|
|
|
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 $$$\int_{2}^{5}\left( 8 x - 5 \right)dx$$$
First, calculate the corresponding indefinite integral: $$$\int{\left(8 x - 5\right)d x}=x \left(4 x - 5\right)$$$ (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.
$$$\left(x \left(4 x - 5\right)\right)|_{\left(x=5\right)}=75$$$
$$$\left(x \left(4 x - 5\right)\right)|_{\left(x=2\right)}=6$$$
$$$\int_{2}^{5}\left( 8 x - 5 \right)dx=\left(x \left(4 x - 5\right)\right)|_{\left(x=5\right)}-\left(x \left(4 x - 5\right)\right)|_{\left(x=2\right)}=69$$$
Answer: $$$\int_{2}^{5}\left( 8 x - 5 \right)dx=69$$$