Calc integrals and volume!

Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=x2 y=25 and x=0 about the y-axis.
x is between 0 and 5


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thank you (:

First sketch the 2-D region.
It is bound on the left by the vertical line x=0
It is bound above by the horizontal line y=25
The third side is the curved line y=x^2, which curves from (0,0) to (5, 25)
So the shape is sort of an upside down sail.

Now you need to rotate this around the y axis. I would use disks: at each y value you find the volume of the disk. Each disc has radius = x = sqrt(y), so if V is volume:
dV = pi * radius^2 * dy
= pi (sqrt(y))^2 dy
= pi y dy

So V = [integrate y from 0 to 25] pi y dy
I'm sure you can do that integral yourself...