Finding the volume of solids..

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!

Re: Finding the volume of solids..

(1) I assume the curve is rotated about the x-axis ...

Re: Finding the volume of solids..

(2) note ...

Re: Finding the volume of solids..

For 2 is it x^6/(x^2+1)^2? I integrated with trig sub and got tan2x-x...please show me how you'd integrate, ibe a feeling im wrong..

Re: Finding the volume of solids..

long division ...

integrating the first three terms is rather straightforward ... I would use the trig substitution for the last term.

Re: Finding the volume of solids..

Thank you!

I wonder if there is something wrong with my method of long division, I got a different answer from yours..

I used partial fractions to tackle the fraction..

Thank you so much, really appreciate your help!

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Re: Finding the volume of solids..

Quote:

Originally Posted by

**Tutu** I wonder if there is something wrong with my method of long division ...

looks that way ...