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This problem I do not get at all...

2nd problem. I did all this

Center is (R,0)

r² = (x-R)² + y² ---eqn of a circle at (R,0)

y = ±√ r² - (x-R)²

f(x) = ±√ r² - (x-R)²

h = √ (r² - (x-R)²) - -√( r² - (x-R)²)

h = 2 √ (r² - (x-R)² )

Interval [a,b ] is [R-r,R+r]

V = 2π∫ x h dx [a,b]

V = 2π∫ x [2 √ (r² - (x-R)² ) ] dx [R-r,R+r]

V = 4π ∫ x √ (r² - (x-R)² ) dx [R-r,R+r]

And so then I integrated the whole thing and got 2R - 4Center is (R,0)

r² = (x-R)² + y² ---eqn of a circle at (R,0)

y = ±√ r² - (x-R)²

f(x) = ±√ r² - (x-R)²

h = √ (r² - (x-R)²) - -√( r² - (x-R)²)

h = 2 √ (r² - (x-R)² )

Interval [a,b ] is [R-r,R+r]

V = 2π∫ x h dx [a,b]

V = 2π∫ x [2 √ (r² - (x-R)² ) ] dx [R-r,R+r]

V = 4π ∫ x √ (r² - (x-R)² ) dx [R-r,R+r]

And so I integrated the whole thing and I got 2R - (4π/3)x(-2r^2 - 4Rr)