Calculadora de integrales definidas e impropias

La calculadora intentará evaluar la integral definida (es decir, con límites de integración), incluyendo las impropias, mostrando los pasos.

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Solution

Your input: calculate $$$\int_{0}^{50}\left( 25 x - 1250 \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\left(25 x - 1250\right)d x}=\frac{25 x \left(x - 100\right)}{2}$$$ (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.

$$$\left(\frac{25 x \left(x - 100\right)}{2}\right)|_{\left(x=50\right)}=-31250$$$

$$$\left(\frac{25 x \left(x - 100\right)}{2}\right)|_{\left(x=0\right)}=0$$$

$$$\int_{0}^{50}\left( 25 x - 1250 \right)dx=\left(\frac{25 x \left(x - 100\right)}{2}\right)|_{\left(x=50\right)}-\left(\frac{25 x \left(x - 100\right)}{2}\right)|_{\left(x=0\right)}=-31250$$$

Answer: $$$\int_{0}^{50}\left( 25 x - 1250 \right)dx=-31250$$$

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Solution