Question

Evaluate : ${\int }_0^1(x+1)dx$

Answer 1

Given : ${\int }_0^1(x+1)dx$

Let $I={\int }_0^1(x+1)dx={\int }_0^{1}xdx+{\int }_0^{1}1dx$

$={\left(\frac{x^2}{2}\right)}_0^1+{\left(x\right)}_0^1$

$=(\frac{1^2}{2}-0)+(1-0)$

$I=\frac{3}{2}$