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 $\displaystyle x = y^2$ and the right curve is $\displaystyle x=2-y$ They intersect at $\displaystyle (1,1). $ The integral is $\displaystyle 2 \pi \int_0^1 y(\underbrace{2-y}_{right\; curve} - \underbrace{y^2}_{right\,curve})\,dy
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