I'm not sure of my comprehension of the problem :s (and for the resolution )
Find the domain for y, helping with x=9-y² and the domain of x. I think that the latter is [-2,0] (symmetric to -1)
The volume will be :
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
, , about the line
:/ Reviewing for a test next week and realize I've forgotten how to do these, tried two different ways with incorrect answers each time (I think my problem is by rotating it around x=-1 instead of an axis, because I just did two of these correctly which were rotated about an axis).
I went ahead and tried it anyway, and got:
The correct answer should be if the back of the book is correct.
Here's the shell method since Angel white done the washer method.
With shells, the cross-sections are parallel to the axis about which we ar rotating. Since x=-1 is vertical, the cross-sections will be 'stacked up' along the x-axis and we can integrate wrt x.
Thank you everyone for helping me out today ^_^
These are things I should have kept up with, but my data structures and algorithms course has been soooooo exciting lately that Calc kind of fell by the wayside :/
Good to be catching up on Calc, though (since I'm 2 weeks ahead in DS&A with nothing else to do)