Posted by **Raven** on Sunday, November 28, 2010 at 12:43pm.

find the area the region bounded by the graphs of the given equation y=81x,y=x^5,x=0,x=3

- calculus -
**MathMate**, Sunday, November 28, 2010 at 1:07pm
The area is between the function y=x^5 and y=81x, between the limits x=0 and x=3.

The functions are all in the first quadrant (no values negative), and the two curves y=81x and y=x^5 intersect at x=3, the upper integration limit, which is a "lucky coincidence".

The area function a(x), is therefore

a(x)=81x-x^5

You would integrate a(x) from 0 to 3 to find the area, thus

Area = ∫a(x)dx [x=0,3]

=∫(81x-x^5)dx [x=0,3]

Here's an image to give you an idea of the area:

http://img11.imageshack.us/img11/6060/1290966183.png

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