Question

Calcule a seguinte integral definida (√√x²)dx O O A B C OD 22/V/3-2/3/2 5 1|5 √/2-1/2 5 3 225/9-1/20 2²2√5-1²/2​

Answer 1

$\displaystyle \sf \underline{\text{integral de{f}inida de um mon{\^o}mio}} \\\\ \int\limits^a_bx^{n}dx = \large {\left \frac{x^{n+1}}{n+1}\right| }\limits^a_b = \frac{a^{n+1}}{n+1}-\frac{b^{n+1}}{n+1} \\\\\\ temos : \\\\ \int\limits^3_1\sqrt[3]{\sf x^2}dx \to \int\limits^3_1 x^{\frac{2}{3}}dx \to \left \frac{\displaystyle x^{\left( \frac{2}{3}+1\right)}}{\displaystyle \frac{2}{3}+1} \right|\limits^3_1$

$\displaystyle \sf \left \frac{x^{\frac{5}{3}}}{\frac{5}{3}}\right|\limits^3_1 =\left \frac{3\cdot \sqrt[3]{\sf x^5 }}{5}\right|\limits^3_1 =\frac{3\cdot \sqrt[3]{3^5}}{5}-\frac{3\cdot \sqrt[3]{1^5}}{5} \\\\\\ \frac{3\cdot \sqrt[3]{3^3\cdot 3^2}}{5} - \frac{3\cdot 1}{5} = \frac{3\cdot 3\cdot \sqrt{9}}{5}-\frac{3}{5} \\\\\\ \huge\boxed{\sf \ \frac{9\sqrt[3]{9}}{5}-\frac{3}{5} \ }\checkmark$

letra C