Which of the following integrals represents the volume of the solid obtained by rotating the region bounded by the curves x^2 - y^2 = 7 and x= 4 about the line y = 9?
A. ∫ from -3 to 3 2π (y - 9) (4 - (√y^2 +7)) dy
B. ∫ from √7 to 4 2π (9 - y) (4 - (sq. root of (y^2+7)) dy
C. ∫ from √7 to 4 2π (y - 9) sq root of (y^2 +7)) dy
D. ∫from √7 to 3 2π (9 - y) (4 - (sq. root of (y^2 +7)) dy
E. ∫ from -3 to 4 ( y + 9) sq. root of (y^2 + 7) dy
F. ∫ from √7 to 4 (Y - 9) ( 4 - (sq. root of (y^2 +7)) dy
G. ∫ from -3 to 3 2π (9 - y) (4 - (sq. root of (y^2 +7)) dy
Here is a graph (without labels) showing the situation described in the problem: it is the lower colored region that is being revolved about $ \ y \ = \ 9 \ $ , while the upper (more faintly) colored region shows the rest of the cross-section of the volume in the $ \ xy-$ plane. The cylindrical shell method is being used for the volume integral, since "slices" for the "wall" of the shell are always parallel to the rotation axis in that method.
Hopefully, this will make clearer which is the correct choice among the ones offered for the question.