1. ## 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 ?

2. 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 $\pi$ ?

3. 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?

4. 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 $2\pi$