SOLUTION: Find the area of theregion enclosed by the graphs of f(x)=2x-5 and g(x)= (-x^2)+6x-5

Algebra ->  Linear-equations -> SOLUTION: Find the area of theregion enclosed by the graphs of f(x)=2x-5 and g(x)= (-x^2)+6x-5      Log On


   

Question 1060674: Find the area of theregion enclosed by the graphs of
f(x)=2x-5 and g(x)= (-x^2)+6x-5
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Graphing the region,
.
.
.
.
.
.
.
So the actual function to integrate is,
g-f=-x%5E2%2B6x-5-2x%2B5
g-f=-x%5E2%2B4x
The limits of integration are x=0 and x=4 so,
A=int%28%28-x%5E2%2B4x%29%2Cdx%2Cx=0%2C4%29
A=-x%5E3%2F3%2B2x%5E2%2BC
A=-4%5E3%2F3%2B2%284%29%5E2
A=-64%2F3%2B32
A=-64%2F3%2B96%2F3
A=32%2F3