The graph of a donut is shown below,

The graph of a donut is shown below,

The graph of a donut is shown below, whose cross-section is a circle with radius r. (1) When

R = 4, r = 2, nd the volume V of the donut. (2) Write down the general expression of the

volume V as a function of R and r.

(1) the equation of the right half of the circle is x = R +

p

r2 y2, while the equation of the

left half of the circle is x = R

p

r2 y2.

(2)

R p

r2 x2dx = x

2

p

r2 x2 + r2

2 arctan(p x

r2 x2 ) + C.

i have uploaded a file of the homework. i missed the classes last week due to illness, so it was very difficult to do the homework. can you please help?