Answer to Question #155572 in Calculus for Samuel kassapa

Question #155572

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


1
Expert's answer
2021-01-19T12:36:55-0500

If f(x)=(1x2+2x3)dx.Find f(x) given that f(2)=2If\ f(x)=(\frac{1}{x^2} +2x -3)dx.\\ Find\ f(x)\ given\ that\ f(2) =2


This means f(x)=x2+2x3f'(x)=x^{-2}+2x-3


Integrate f(x)f'(x) :

f(x)=x2+2x3,1x2dx+2xdx3dx=1x+x23x+cf(x)=1x+x23x+c,But f(2)=2f(2)=2=12+223(2)+c,c=92    f(x)=1x+x23x+92f'(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}\\



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment