# Math Help - Method of cylindrical shells

1. ## Method of cylindrical shells

Could anyone help me set up this integral?

Question:
Use the cylindrical shell method to find the volume of the solid using the region bound by these curves about the x-axis;

y=√x , y=0 , x+y=2

Thank you!!

2. Originally Posted by klooless
Could anyone help me set up this integral?

Question:
Use the cylindrical shell method to find the volume of the solid using the region bound by these curves about the x-axis;

y=√x , y=0 , x+y=2

Thank you!!
Since you want shells about the x-axis, the integration variable is y (draw a picture). The left curve is $x = y^2$ and the right curve is $x=2-y$ They intersect at $(1,1).$ The integral is $2 \pi \int_0^1 y(\underbrace{2-y}_{right\; curve} - \underbrace{y^2}_{right\,curve})\,dy
$

3. Thank danny! I've got it!