Question

Propriedades da Integral definida
$\int\limits^2_1 { \frac{5}{8x^6} }$

Answer 1

$\int\limits^2_1 \frac{5}{8x^6} \, dx =\frac{5}{8} \int\limits^2_1 x^{-6} \, dx\\\\ \frac{5}{8}*\frac{x^{-6+1}}{-6+1} = \frac{5}{8}*\frac{1}{5x^5}=\boxed{-\frac{1}{8x^5}}\\ \\\ \int\limits^2_1 \frac{5}{8x^6} \, dx =(-\frac{1}{8*2^5})-(-\frac{1}{8*1^5})\\\\\ \int\limits^2_1 \frac{5}{8x^6} \, dx = -\frac{1}{256}+\frac{1}{8}\\ \\ \large\boxed{ \int\limits^2_1 \frac{5}{8x^6} \, dx =\frac{31}{256}}$