Calculus 1 Help
posted by Anonymous on .
Find the volume generated by rotating about the given line
a) y^2=x, x=2y; about the yaxis
b) y=x, y=sqrtx; about y=1

(a)
using shells of thickness dx,
v = ∫[0,4] 2πrh dx
where r=x and h=√xx/2
v = ∫[0,4] 2πx(√xx/2) dx = 64π/15
using discs of thickness dy,
v = ∫[0,2] π(R^2r^2) dy
where R=2y and r=y^2
v = ∫[0,2] π((2y)^2y^4) dy = 64π/15
Now you try (b), recalling the formulas for volumes of discs and shells, above. Sketch the curves and figure out the radius or height.