Question

Como resolver a integral $\pi \int\limits^8_0( \sqrt[3]{y} ) ^{2} \, dy$

Answer 1

$\pi \int\limits^8_0 { (\sqrt[3]{y})^{2} } \, dy = \pi \int\limits^8_0 { y^{ \frac{2}{3} } } \, dy = \\ = \frac{3 \pi }{5} [{8^{ \frac{5}{3}} - 0] = \frac{32.3 \pi }{5} = 60,32 u.v.$