(1) I assume the curve is rotated about the x-axis ...
Hi this is regarding volume of solids, it's the basics but I can't get the answers and it's frustrating me! Any help will be very much appreciated, really!
1.) Find the volume of solid formed when y= is rotated for
I integrated from 1 to 3 and got 12pi units^3 as the answer, my answer after integration was pi( ..I can't see any possible errors in my working, I must have integrated wrongly..
2.) Find the volume of solid formed when y= is rotated for xE[1,3]
I integrated from 1 to 3.
I chose to use trig substitution, so I got
I had changed to since I thought , then ..
Simplifying, I ended up with
Also, I thought since , then
so I got ..
Separating into two integrals and changing tan to sec again, I ended up with
..
Integrating I got
, from 1 to 3..
Are my steps correct so far?
3.) A hemispherical bowl of radius 8cm is filled to a depth of 3cm. Find the volume of water in the bowl. The equation is
I integrated from 0 to 3, the equation ..
Please assist me I really am at a loss as to why my answers are all wrong..
Thank you very much!