Question

Qual é o valor da integral definida de

Answer 1

$\displaystyle \int\limits^3_0 \sqrt{\text x+1}\text{dx} \\\\\\ \underline{\text{Fa{\c c}amos}}: \\\\ \text u =\text x +1 \to \text {du} = \text {dx} \\\\\\ \int\limits^{3}_0\sqrt{\text u}\text{dx} \to \int\limits^3_0 \text u^{\displaystyle (\frac{1}{2})} \text{du} \\\\\\ \left[\begin{array}{c}\frac{\displaystyle \text u^{\displaystyle (\frac{1}{2}+1)}}{\displaystyle \frac{1}{2}+1}\end{array}\right]\limits^3_0$

$\displaystyle \left[\begin{array}{c}\frac{\displaystyle 2.\text u^{\displaystyle (\frac{3}{2})}}{\displaystyle 3}\end{array}\right]\limits^3_0 \\\\\\\\ {\ [\frac{2\sqrt{(\text x+1)^3}}{3} \ ]\limits^3_0 \to \frac{2\sqrt{(3+1)^3}}{3} - \frac{2\sqrt{(0+1)^3}}{3} } \\\\\\ \frac{2\sqrt{4^3}}{3} -\frac{2}{3} \to \frac{2.8}{3}-\frac{2}{3} \\\\\\ \frac{16-2}{3} \\\\\\ \huge\boxed{\ \frac{14}{3}\ }\checkmark$

Letra b