# Volume of solids

• Mar 22nd 2009, 04:02 PM
nyasha
Volume of solids
Consider region enclosed by the curves y=sinx and and y=0 for x between 0 and $\pi$.Find the volume of the solid obtained when this region is revolved about the y-axis.

Attempt to solution:

Use shells method

$r=x-0$

$v=2\pi\int_0^{\pi} xsinx dx$

Use integration by parts

$\int udv=-xcosx+\int cosx dx$

$\int udv=2\pi(-xcosx+sinx)$

How come the answer book is saying l am wrong ? What did l do wrong ?
• Mar 22nd 2009, 04:30 PM
skeeter
Quote:

Originally Posted by nyasha
Consider region enclosed by the curves y=sinx and and y=0 for x between 0 and $\pi$.Find the volume of the solid obtained when this region is revolved about the y-axis.

Attempt to solution:

Use shells method

$r=x-0$

$v=2\pi\int_0^{\pi} xsinx dx$

Use integration by parts

$\int udv=-xcosx+\int cosx dx$

$\int udv=-xcosx+sinx$

How come the answer book is saying l am wrong ? What did l do wrong ?

I tried really hard, but i just couldn't see your answer book on my PC screen.

so, did you evaluate the definite integral from $0$ to $\pi$ ?
• Mar 22nd 2009, 04:36 PM
pedromartinez
Quote:

Originally Posted by nyasha
Consider region enclosed by the curves y=sinx and and y=0 for x between 0 and $\pi$.Find the volume of the solid obtained when this region is revolved about the y-axis.

Attempt to solution:

Use shells method

$r=x-0$

$v=2\pi\int_0^{\pi} xsinx dx$

Use integration by parts

$\int udv=-xcosx+\int cosx dx$

$\int udv=-xcosx+sinx$

How come the answer book is saying l am wrong ? What did l do wrong ?

when you reflect it you get a cylinder, unroll it to make a rectangle and the dimensions are 2piX by sinx

multiply them and take out the 2pi

2pi (XsinX)

then integrate on your calculator or by hand

either way the answer should be

19.739 or 6.28 pi

is that right?
• Mar 22nd 2009, 05:17 PM
nyasha
Quote:

Originally Posted by skeeter
I tried really hard, but i just couldn't see your answer book on my PC screen.

so, did you evaluate the definite integral from $0$ to $\pi$ ?

I had evaluated from $0$ to $\pi$ but l forgot to multiply by $2\pi$(Headbang)(Headbang)(Headbang)(Headbang)(Headbang)