Integration and Volumes?

[OhhCalculus]

So, I need to graph (with my calculator) this out, and then find the area, and finally the volume.

y=(x-1)^1/2, y=0, x=2, x=5; about the x-axis

I ended up with some crazy answer like 10?, and I know that's incorrect. I'm supposed to be doing the washer method.

 

[tkhunny]

What's wrong with \(\displaystyle 10\pi\)? Just a quick estimate - suppose it is a straight line, rather than a curve between y = 1 and y = 2. This would give around: \(\displaystyle \pi\cdot \left(\frac{3}{2}\right)^2\cdot 3\;=\;\frac{27}{4}\pi\). Well, okay, that's quite a bit less than \(\displaystyle 10\pi\), but it IS in the neighborhood.

I like to do it with Shells AND Washers, to learn the relationship and to gain experience in knowing which might be easier in a specific case.

In this case, Washers if MUCH easier. Here's Shells.

\(\displaystyle \int_{0}^{1}2\cdot\pi\cdot y\cdot 3\;dy\;+\;\int_{1}^{2}2\cdot\pi\cdot y\cdot\left[5-(y^{2}+1)\right]\;dy\)

Give it another go and show us what you get.