Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. Find the volume V of this solid.

y=x^5, y=x, x greater than or equal to 0.

Question

Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. Find the volume V of this solid.

y=x^5, y=x, x greater than or equal to 0.

anonymous · Answer

I have integral from 0 to 1of pi((x)^2-(x^5)^2) like the formula but that ends up equaling zero. Do I need to split the integral or something?

anonymous · Answer

Monkyman640, is this in inequalities?

anonymous · Answer

No, this is cal 2.

anonymous · Answer

Volume of a solid.

anonymous · Answer

The inequality just sets the limits of integration.

amistre64 · Answer

|dw:1349206906533:dw|

amistre64 · Answer

does the x >=0 mean that we define the setup as the crossing points?  or does this extend beyond into infinity?

anonymous · Answer

It should mean that the integral is evaluated from 0 to the intersection point, which should be 1.

amistre64 · Answer

oh good :)  cause i really couldnt see it being finite the other way

amistre64 · Answer

there are 2 ways to view this; you can take the volume of the top function and then remove or carve out the volume of hte bottom function; or you can try as you did and place them together in some amlagamation of R^2-r^2