SOLUTION: Find the area of the region bounded by the curve y = 5x — x2., x =0, x = 5 and lying above the x-axis.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the area of the region bounded by the curve y = 5x — x2., x =0, x = 5 and lying above the x-axis.      Log On


   

Question 440073: Find the area of the region bounded by the
curve y = 5x — x2., x =0, x = 5 and lying
above the x-axis.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Looking at the graph:
graph%28+300%2C+300%2C+-7%2C+7%2C+-7%2C+7%2C+5x+-+x%5E2+%29
The parabolic segment of which we want the area has width w = 5, and height h = 25/4.
Hence by the formula of a parabolic segment,
A+=+%282%2F3%29wh+=+%282%2F3%29%2A5%2A%2825%2F4%29+=+125%2F6 square units.
If we used integral, we get the same area value:

=125%2F2+-+125%2F3+=+125%2F6