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 $$$\int_{0}^{2}\left( \sqrt{y} \right)dy$$$

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

$$$\left(\frac{2 y^{\frac{3}{2}}}{3}\right)|_{\left(y=2\right)}=\frac{4 \sqrt{2}}{3}$$$

$$$\left(\frac{2 y^{\frac{3}{2}}}{3}\right)|_{\left(y=0\right)}=0$$$

$$$\int_{0}^{2}\left( \sqrt{y} \right)dy=\left(\frac{2 y^{\frac{3}{2}}}{3}\right)|_{\left(y=2\right)}-\left(\frac{2 y^{\frac{3}{2}}}{3}\right)|_{\left(y=0\right)}=\frac{4 \sqrt{2}}{3}$$$

Answer: $$$\int_{0}^{2}\left( \sqrt{y} \right)dy=\frac{4 \sqrt{2}}{3}\approx 1.88561808316413$$$

Calculadora de Integrais Definidas e Impróprias

Calcule integrais definidas e impróprias passo a passo

Solution