Find the volume of a solid from the following Please explain

Find the volume of a solid from the following:

Please explain the process in DETAIL. I don\'t want an answer, but I want an explanation of how to do this. Thank you.

Solution

at x = /3, y = 2
V = integral of 2rf(y)dy........limit from 0 to 2
r = (3-y)
f(y) = sec^-1(y)
V = integral of 2(3-y)sec^-1(y)dy
V = integral of [6 - 2sec^-1(y)]dy
integrating wrt y
V = 6 integral of dy - 2sec^-1(y)integral of dy + integral of (d/dx(sec^-1(y)) * integral of dy)
V = 6y - 2ysec^-1(y) + integral of [1/yy^2-1 * y]
V = 6y - 2ysec^-1(y) + integral of [1/y^2-1]
V = 6y - 2ysec^-1(y) + ln|y + y^2-1|
apply limits
V = 12 - 4*/3 + ln|2 + 3|
V = 12 - 4/3 ^2 + ln|2+3|