Question

Evaluate:

${\int }_0^1{x}^3+3x^{2}dx$

Answer 1

${\int }_0^1{x}^3+3x^{2}dx$

$={\int }_0^1{x}^{3}dx+{\int }_0^{1}3x^{2}dx$

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

=${\frac{x^4}{4}+x^3|}_0^1$

$=\frac{1}{4}+1=\frac{5}{4}$