Calculus II question, I am having difficulty setting up disk, washer and shell problems. I did the single volumes, but the offset rotations and multiple formula transitions are slipping me up. I can get the integral solution once it is set up, but I am having difficulty setting them up.

Find the volume of the solid obtained by rotating the region between y=x^2 and the Y-axis in the area 0

Question

Calculus II question, I am having difficulty setting up disk, washer and shell problems. I did the single volumes, but the offset rotations and multiple formula transitions are slipping me up. I can get the integral solution once it is set up, but I am having difficulty setting them up.

Find the volume of the solid obtained by rotating the region between y=x^2 and the Y-axis  in the area 0<x<2, about x = -4.


Find the volume of the solid obtained by rotating the region between y=x^2 and the Y-axis  in the area 0<x<2, about y = 0.

amistre64 · Answer

shift the equations so that they rotate around the x or y axis

amistre64 · Answer

x=-4 need to move +4 to get to the y axis

(x-4)^2  should do the trick

amistre64 · Answer

and of course the x=0 axis moves to x=4 :)

amistre64 · Answer

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amistre64 · Answer

you sure you got this question right?

anonymous · Answer

I forgot it was x^2+2, but I think I found my mistake for the (x-4) portion, I think that is the one I have to reverse as an equation in the form of x=sqrt(y-2)?

amistre64 · Answer

perhaps; but as is; you have no cap on this thing

amistre64 · Answer

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