Question

volume of a region bounded by x=-y^2 +4 and x=0; revolved about x=-1

Answer 1

1. solve for y in terms of x. this is R(x)
1a. since 0 is 1 step away from x = 1 call this r
2. take the integral of this R^2 - r^2 dx
3. multiply the result by pi.
4. find where R and r interect. these are your bounds for the integral

Answer 2

Did that still got it wrong

Answer 3

my bad it looks like your rotating the other way inegrate this: (-y^2 + 4 ) ^2 - 1 dy
your bounds of integration will be the values of y where x = 0 and the parabola intersect. then mutliply by pi.

Answer 4

It looks like you are doing washer method, which does not look appropriate for this case.

Answer 5

Correction washer merit is appropriate

Answer 6

Bounds of integration 0 to 2. Integrate [(-y^2+4)^2 pi - 1^2 pi]