- #1
Gundown64
- 9
- 0
Homework Statement
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = 5x, y = 5[itex]\sqrt{x}[/itex] about y = 5
Homework Equations
A(x)=∏(R2-r2)
The Attempt at a Solution
A(x)=∏(5x)2-(5[itex]\sqrt{x}[/itex])2)
A(x)=∏(25 x2 - [itex]\frac{10}{3}[/itex]x[itex]\frac{3}{2}[/itex])
V=∏[itex]\int[/itex][itex]^{1}_{0}[/itex](25x2- [itex]\frac{10}{3}[/itex]x[itex]\frac{3}{2}[/itex])dx
V=∏([itex]\frac{25}{3}[/itex]x3-[itex]\frac{4}{3}[/itex]x[itex]\frac{5}{2}[/itex]) {0,1}
V=∏([itex]\frac{25}{3}[/itex]-[itex]\frac{4}{3}[/itex])
V= [itex]\frac{21}{3}[/itex]∏
Where did I go wrong? I can't figure out the about y=5. If I am correct, you would usually subtract 5 from the two radii, but since they intersect at y=5, the just flip on that intersection point and thus we don't need to find the lost area. Bad explanation, I know, maybe someone can explain it to me.
Thanks in advance!