Question

Решить интеграл s= ∫(с низу 1 до 2) (2/x^2-4x^2)dx= ?

Answer 1

$\int\limits^2_1 {( \frac{2}{ x^{2} } -4 x^{2} )} \, dx = \int\limits^2_1 {(2* x^{-2}-4 x^{2} )} \, dx =2* \frac{ x^{-2+1} }{-2+1}| _{1} ^{2} -4* \frac{ x^{2+1} }{2+1} | _{1} ^{2} =$
$=- \frac{2}{x} | _{1} ^{2} - \frac{4 x^{3} }{3} | _{1} ^{2} =-( \frac{2}{2}- \frac{2}{1} )-( \frac{4* 2^{3} }{3} - \frac{4* 1^{3} }{3} )=-(1-2)-( \frac{32}{3} - \frac{4}{3} )=$
$=1- \frac{28}{3} =1-9 \frac{1}{3} =-8 \frac{1}{3}$