Answer to Question #104687 in Calculus for abdullah

Question

x^3-\frac{2}{x^2}+2
(1,3)

Answer 1

$\int^3_1(x^3-{2\above{2pt} x^2}+2)dx$

$=({x^4 \above{2pt} 4}-{2 \above{2pt} -x}+2x)|^3_1$ =$2(x^{-2})$ =$2({x^{-2+1}\above{2pt} -2+1})$

$=({3^4-1^4\above{2pt} 4}-2(-{1\above{2pt} 3}+{1 \above{2pt} 1})+2(3-1))$

$=({80-1 \above{2pt} 4}-2({-1+3 \above{2pt} 3})+2(3-1))$

$=({80 \above{2pt} 4}-{4\above{2pt} 3}+4)$

$=(20-{4 \above{2pt} 3}+4)$

$=({60-4+12\above{2pt} 3})$

$={68 \above{2pt} 3}$

Answer: $\frac{68}{3}.$