Answer to Question #155572 in Calculus for Samuel kassapa

Question

If f(*)=$(1/*^2 +2* -3)d* find f(*) given that f(2) =2

Answer 1

$If\ f(x)=(\frac{1}{x^2} +2x -3)dx.\\ Find\ f(x)\ given\ that\ f(2) =2$

This means $f'(x)=x^{-2}+2x-3$

Integrate $f'(x)$ :

$f'(x)=x^{-2}+2x-3,\intop\frac{1}{x^2}dx+\intop 2xdx-\intop 3dx=-\frac{1}{x}+x^2-3x+c\\ f(x)=\frac{1}{x}+x^2-3x+c,\\ But\ f(2)=2\\ f(2)=2=\frac{1}{2}+2^2-3(2)+c,\\ c=\frac{9}{2}\\ \implies f(x)=\frac{1}{x}+x^2-3x+\frac{9}{2}\\$