Calcolatore di integrali definiti e impropri

Il calcolatore cercherà di valutare l'integrale definito (cioè con estremi), inclusi quelli impropri, mostrando i passaggi.

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If you need `-oo`, type -inf.

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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: $$$\int_{2}^{5}\left( 8 x - 5 \right)dx=69$$$

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Solution