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AP Calculus Help (Last Time xD)

OLD_SCHOOL_PLAYER

New Member
I just need help with two more AP Calculus problems, and then I'll be done for the year.


Find volume of region generated by rotating shaded area about the x-axis:

y = 3 - (6/x)

x = 5

Window:
x min: 0
x max: 6
y min: 0
y max: 2

This is what I did for this problem, not completely sure if I did this correctly:
y = 3 - (6/x), x = 5
nr^2
pi INTEGRAL(from 2 to 5) [ (3-(6/x))^2 ]
=15.122

The second problem:

The base of a solid is the region between the line y = 4 and parabola y = x^2. The cross sections perpendicular to x-axis are semicircles, find volume of solid.



Thank you for taking the time to read this,
OSP
 
Its been a while, so someone should correct my mistakes but...
For the first question, the shape starts at 2 (where y=0) and ends at x=5. Area of a circle is piR^2 so I'm thinking it would be the integral from 2 to 5 of pi((3 - (6/x))^2). You can evaluate that.

Some one else check this. The second question is similar.
 
First one looks right.

Second one:

PI[integral(-2 to 2) of (x^2/2)^2]


I did this all in my head but that should be right.

edit: yeah Frankie that's what he had for the 1st one
 
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