OK - I'll do one more, then it's your turn
using shells of thickness dy, we have
v = ∫[0,2] 2πrh dy
where r = 3-y and h = 5-x = 5 - (y^2+1)
v = ∫[0,2] 2π(3-y)(5-(y^2+1)) dy = 24π
you can check your answer using discs of thickness dx:
v = ∫[1,5] π(R^2-r^2) dx
where R = 3 and r = 3-y = 3-√(x-1)
v = ∫[1,5] π(3^2-(3-√(x-1))^2) dx = 24π
Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the line y=3.
y=√x-1 ,y=0 ,x=5
4 answers
Question, where did the 3-y come from. Also, I will do the beginning of the other problem I requested help for, but I am trying to understand how you got 3-y. I understand how you got your height, but not the 3-y.
the axis of rotation is y=3, but the graph is some distance away from it. The radius of the shells is the distance from the curve to the axis of rotation.
Did you not sketch the curves in question?
Did you not sketch the curves in question?
I did, but I wasn't sure if I was supposed to subtract the y from the axis of rotation. I was in doubt of myself on that one. I understand.