volume of this solid

Question

i dont know how to solve this problem : find the volume of the region bounded by x = 1 − y^2 ,x = 2 + y^2, y = −1, y = 1, is revolved about the y-axis ! thank you

Answer 1

Hi Marcio,

 

The easiest way to solve this problem is to use the washer method, but integrating along the y-axis. The problem has already solved the for x in terms of y. Remember "outer radius squared minus inner radius squared".

 

This graph should give you the idea:

 

https://www.desmos.com/calculator/wzoet1ootl

 

Focus on lines 13, 15, and 16.