AP Calculus AB Integral Volume Question

Question

The region in the first quadrant bounded by x² + 4y² = 64, the x-axis, and the y-axis is revolved around the y-axis. What is the volume of the solid?

Answer 1

Use the disk method around the y axis: Integral from x = 0 to y₀ of πx(y)²dy where you are stacking disks of area πx² of height dy from y= 0 to y intercept (where x =0 and 4y² = 64, y = 4)

volume is the Integral from y = 0 to 4 of π(64-4y²)dy which is easily integrable.