1:
(a) Observe that the solid obtained by rotating
about the x-axis is a sphere of radius r.
(b) Find the volume of this solid of revolution. Does it coincide with the known formula for the volume of a sphere?
(c) (Bonus) Observe that the solid obtained by rotating the region bounded by
and the line x = h and the x-axis, about the x-axis, is a cone of radius r and height h. Find the volume of this solid of revolution. Does it coincide with the known formula for the volume of a cone?
2: Use integration by parts to compute the following indefinite integrals:
3: The goal of this problem is to find fe* cos(æ) dx.
(a) Prove that
by integration by parts.
(b) Again by integration by parts, prove that
(c) Deduce that
(d) (Bonus) Proceed similarly to calculate fe sin(x) dx.