- #1
dlacombe13
- 100
- 3
Homework Statement
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.
y=x2
x=y2
Rotated about y=1
Homework Equations
Area of cross-section (in this case, a disk) = A(x) = π(outer radius)2 - π(inner radius)2
Volume = V = ∫A(x) dx
The Attempt at a Solution
[/B]
yellow line => y=x2
red line => x=y2
I converted x=y2 to y=√x
The outer-radius is y=x2
The inner-radius is x=√x
The intersection points of the two graphs is (0,0) and (1,1)
So A(x) = π(x2)2 - π(√x)2 = π(x4-x)
So V = ∫A(x)dx = π ∫ [ (1/5)x5 - (1/2)x2 ]dx integrated at (x=0 to x=1) = -3π/10 ...
However the volume can't be negative and the correct answer is 11π/30
Any help? The book shows the same graph and same intersection points, but I am getting the wrong answer.