Calculadora de Integrais Definidas e Impróprias

A calculadora tentará calcular a integral definida (isto é, com limites), inclusive no caso impróprio, com os passos mostrados.

Enter a function:

Integrate with respect to:

Enter a lower limit:

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

Enter an upper limit:

If you need `oo`, type inf.

Please write without any differentials such as `dx`, `dy` etc.

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Solution

Your input: calculate $$$\int_{1}^{3}\left( \frac{4 x^{2} - 3}{x^{2}} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\frac{4 x^{2} - 3}{x^{2}} d x}=4 x + \frac{3}{x}$$$ (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.

$$$\left(4 x + \frac{3}{x}\right)|_{\left(x=3\right)}=13$$$

$$$\left(4 x + \frac{3}{x}\right)|_{\left(x=1\right)}=7$$$

$$$\int_{1}^{3}\left( \frac{4 x^{2} - 3}{x^{2}} \right)dx=\left(4 x + \frac{3}{x}\right)|_{\left(x=3\right)}-\left(4 x + \frac{3}{x}\right)|_{\left(x=1\right)}=6$$$

Answer: $$$\int_{1}^{3}\left( \frac{4 x^{2} - 3}{x^{2}} \right)dx=6$$$

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Calculadora de Integrais Definidas e Impróprias

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Solution