SOLUTION: Let R be the region enclosed by the graph of : F(x)=5x and g(x)=(X^2)+3x-3 Find the area of the region R

Algebra ->  Linear-equations -> SOLUTION: Let R be the region enclosed by the graph of : F(x)=5x and g(x)=(X^2)+3x-3 Find the area of the region R      Log On


   

Question 1044356: Let R be the region enclosed by the graph of :
F(x)=5x and g(x)=(X^2)+3x-3
Find the area of the region R
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First, find the intersection points.
They will be the limits of integration.
x%5E2%2B3x-3=5x
x%5E2-2x-3=0
%28x-3%29%28x%2B1%29=0
Two solutions,
x-3=0
x=3
and
x%2B1=0
x=-1
.
.
.
.
.
.
.
So integrate between x=-1 and x=3
A=int%28%28f%28x%29-g%28x%29%29%2Cdx%2Cx=-1%2C3%29
A=int%285x-x%5E2-3x%2B3%29%29%2Cdx%2Cx=-1%2C3%29
A=int%282x-x%5E2%2B3%29%29%2Cdx%2Cx=-1%2C3%29
A=x%5E2-x%5E3%2F3%2B3x%2BC%29
A=%283%5E2-3%5E3%2F3%2B3%283%29%29-%28%28-1%29%5E2-%28-1%29%5E3%2F3%2B3%28-1%29%29
A=%289-9%2B9%29-%281%2B1%2F3-3%29
A=%289%29-%28-5%2F3%29
A=32%2F3