Question

Solve ${\int }_1^3(3x^2+1)dx$

Answer 1

${\int }_1^3\left(3x^2-1\right)dx$

$={\int }_1^{3}3x^{2}dx-{\int }_1^{3}dx$

$=3{\int }_1^3{x}^{2}dx-{\int }_1^{3}dx$

$=3{\left[\frac{x^3}{3}\right]}_1^3-{\left[x\right]}_1^3$

$=\left[3^3-1^3\right]-\left[3-1\right]$

$=27-1-2=24$