代写Mathematics Midterm代写C/C++程序

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.