Hi, how do I solve this question?
Let R be the region that is bounded by the triangle with the vertices (0,0), (3, 0), and (1, 1).
Find the volume of the solid generated by revolving the region R about the line x = 3.
Thanks.
sketch a diagram ...
region is bounded by the lines $\displaystyle y=x$ , $\displaystyle y = 0$ , and $\displaystyle y = \frac{3-x}{2}$
rotating about the line x = 3, you can use cylindrical shells w/r to x (will require two integral expressions) or you can use disks w/r to y.
Hi codfire
You need to consider the axis of rotation. It's rotated about x = 3, not x = 0.
The formula : $\displaystyle V=\pi \int^a_b (x-k)^2~dy$ , where k is the axis of rotation.
And you also need to see which curves cover the larger volume after rotated, is it $\displaystyle y=x$ or $\displaystyle y = \frac{3-x}{2}$ ?