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 $$$\int_{2}^{4 s}\left( \frac{t^{3}}{2} \right)dt$$$

First, calculate the corresponding indefinite integral: $$$\int{\frac{t^{3}}{2} d t}=\frac{t^{4}}{8}$$$ (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.

$$$\left(\frac{t^{4}}{8}\right)|_{\left(t=4 s\right)}=32 s^{4}$$$

$$$\left(\frac{t^{4}}{8}\right)|_{\left(t=2\right)}=2$$$

$$$\int_{2}^{4 s}\left( \frac{t^{3}}{2} \right)dt=\left(\frac{t^{4}}{8}\right)|_{\left(t=4 s\right)}-\left(\frac{t^{4}}{8}\right)|_{\left(t=2\right)}=32 s^{4} - 2$$$

Answer: $$$\int_{2}^{4 s}\left( \frac{t^{3}}{2} \right)dt=32 s^{4} - 2$$$

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Calculadora de Integrais Definidas e Impróprias

Calcule integrais definidas e impróprias passo a passo

Solution