Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
x+y=2
x=3–(y–1)^2
about the x-axis.
What I did was solve for x for both equations and made them equal to each other and tried to find the points of intersection, but I don't think i'm doing it correctly. Can someone elaborate on what I should do and the steps involved.
I'm not sure on whether to apply the shell or disc method to find the answer as well.
I'm also confused as to when it says, for example, "about the x-axis." Do I solve looking for y or x?
Thank you.
... and where else? And have you imagined it revolving so you can clearly see (imagine) the solid? Then think of a Reimman strip inside the area - horizontal or vertical, it's up to you. But then imagine the strip rotating, first around one axis, then the other. One way you should see a disk or washer, the other way a cylinder. One is contained nicely in the target solid - choose that method.
Of course, if your strip was vertical, you're using y = f(x) in the chosen formula, horizontal, then x = g(y).
Ah ok. Thank you! I hope it wasn't in the read here first topics lol. If it was, my apologies. So, I finally calculated the answer, but I seemed to still get it wrong. I computed 51pi for my answer, but it's wrong it says.
I think I'm doing something wrong when I'm deriving the equation that you gave me.
I got y^2/2[3y - y^3 -3y^2 +3y/3] - (2y - y^(2)/2). Then I plugged 0 and 3 into it and got my answer like that. Any input on what i'm doing wrong?