Volume of Revolution: Find the Volume from y = x+6 & y = x^2 - 4x

[songoku]

Homework Statement

The line y = x + 6 meets the curve y = x²-4x at the points P and Q. Find the volume of the solid generated when the area enclosed by the line and the curve is rotated through 360^o about the x-axis

Homework Equations

Integration

The Attempt at a Solution

I've drawn the graph and found the intersections, which are x = -1 and x = 6. The region are located in first, second, and fourth quadrants. I'm confused about the region in fourth quadrant.
How to find the volume of all the region when they are rotated 360^o about the x-axis? I can't imagine what shape it forms, I think the region in fourth quadrant will "overlap" with region in first quadrant when rotated.

Thanks

 

[tiny-tim]

hi songoku!

yes, you're right … that doesn't make sense

is that the whole question? I'm wondering why they bothered to give points P and Q names

 

[songoku]

hi songoku!

yes, you're right … that doesn't make sense

is that the whole question? I'm wondering why they bothered to give points P and Q names

hi tiny-tim!

Yes, that's the whole question. I just noticed that we don't need P and Q, just say "the area enclosed by the line and the curve" is enough.

For now, let's assume there is mistake in the question

Thanks tiny-tim!