Verified answer

First off, graph the two regions on your graphing calculator

You will notice the upper bound line is f(x) = x^2 - 4x

and the lower bound line is g(x) = 2x -5

To find the area, you simply take the integral of upper bound minus lower bound.

Also, you will notice on the graph that the points of intersection are at x=1, and x=5

So the limit of integration will be from x=1 to x=5.

Finding area:

Area = [from x=1 to x=5] ʃ [(2x - 5 ) - (x^2 - 4x)] dx

A = [x=1 to x=5] ʃ (-x^2 + 6x - 5) dx

Now take the integral.

A = [-x^3/3 + 6x^2/2 - 5x] x=1 to x=5

A = [-(5)^3/3 + 6(5)^2/2 - 5(5)] - [-(1)^3/3 + 6(1)^2/2 - 5(1)]

A = 32/3 or 10.67

Hope this helps. :)

x^2 − 4x = 2x − 5

x^2 − 6x + 5 = 0

(x - 1) (x - 6) = 0

x1 = 1; x2 = 6

g(x1) = 2(1) - 5 = -3

g(x2) = 2(6) - 5 = 7

draw the curve f(x)

draw the line g(x)

g(x) will cut f(x) at (1,-3) and (6,7)

g(x) is above f(x)