Calculadora de integrales definidas e impropias
Calcular integrales definidas e impropias paso a paso
La calculadora intentará evaluar la integral definida (es decir, con límites de integración), incluyendo las impropias, mostrando los pasos.
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: $$$\int_{0}^{2}\left( \sqrt{y} \right)dy=\frac{4 \sqrt{2}}{3}\approx 1.88561808316413$$$