Question

Evaluate $\underset{1}{\overset{2}{\int }}\log xdx.$

Answer 1

${\int }_1^2$1.log x dx.

$logx.\int 1dx-\int \frac{1}{x}.x.dx.$

$\Rightarrow [xlogx-x{]}_1^2$

$\Rightarrow (2log2-2)-(0-1)$

$\Rightarrow 2log2-2+1\Rightarrow log4-1$