Question

Evaluate : ${\int }_{10}^2(x^2+x+2)dx$

Answer 1

${\int }_{10}^2(x^2+x+2)dx$

$={[\frac{x^3}{3}+\frac{x^2}{2}+2x]}_{10}^2$

$=\frac{1}{3}(1000-8)+\frac{1}{2}(100-4)+2(10-2)$

$=\frac{992}{3}+\frac{96}{2}+2\times 8$

$=\frac{992}{3}+48+16$

$=\frac{992}{3}+64$

$=\frac{1184}{3}$