Question

How do you do this question?

Answer 1

∫₋₃¹ π y⁴ dy

Explanation:

If we slice the solid shape, we get circular cross sections or disks. The thickness of each disk is dy. The radius of each disk is x. So the volume of each disk is:

dV = π r² h

dV = π x² dy

Since x = y²:

dV = π y⁴ dy

The total volume is the sum of all the disks from y=-3 to y=1.

V = ∫ dV

V = ∫₋₃¹ π y⁴ dy