Closed Areas

To find the area of the region enclosed by the curves y=10x-x² y y=3x-8

We resolve the system and we can find the intersection of the graphs:

y=10x-x²

y=3x-8

So we get the equation: 3x-8 = 10x-x2 with a solution of x = 8 and x = -1

We have to realize that at x = 0 the equation is

10x-y = x2 and y = 0 gives y = 3x-8 results in y = -8

Being continuous: 10x-x2 ≥ 3x-8 in [-1,8]

Then we can calculate the area:

Hermes T.