Question

Evaluate:

${\int }_0^1{x}^2+2x$ dx

Answer 1

${\int }_0^1{x}^2+2xdx$

$={\int }_0^1{x}^{2}dx+{\int }_0^{1}2xdx$

By using $\int x^{n}dx=\frac{x^{n+1}}{n+1}+c$

$={\frac{x^3}{3}+x^2|}_0^1$

$=\frac{1}{3}+1=\frac{4}{3}$