Question

resolução da integral definida:

integral de √x dx sob os intervalos 4 e 1

Answer 1

$\int\limits^4_1 { \sqrt{x} } \, dx \\\\= \int\limits^4_1 { x^{ \frac{1}{2} } } \, dx = \left \frac{x^{ \frac{1}{2}+1 }}{ \frac{1}{2}+1 } \right]^4_1 = \left \frac{x^{ \frac{3}{2} }}{ \frac{3}{2} } \right]^4_1 = \left \frac{2* x^{ \frac{3}{2} }}{3} \right]^4_1 = \left \frac{2}{3} * \sqrt{x^3} \right] ^4_1\\\\\\ = \frac{2}{3}*\left( \sqrt{4^3}- \sqrt{1^3} \right) = \frac{14}{3}$