Question

Evaluate the integral
${\int }_4^5(x^2-12x+8)dx$

Answer 1

Formula: ${\int }_a^b{x}^{n}dx=|\frac{x^{n+1}}{n+1}{|}_a^b$

${\int }_4^5(x^2-12x+8)dx$

$\Rightarrow |(\frac{x^3}{3}-\frac{12x^2}{2}+8x){|}_4^5$

$\Rightarrow |(\frac{x^3}{3}-6x^2+8x){|}_4^5$

$\Rightarrow \left(\frac{5^3-4^3}{3}\right)-6\times (5^2-4^2)+8\times (5-4)$

$\Rightarrow \frac{61}{3}-54+8$

$\Rightarrow \frac{-77}{3}$

Therefore, ${\int }_4^5(x^2-12x+8)dx=\frac{-77}{3}$