Homework Help: Trig simplifycation and Intergration

1. Oct 1, 2006

lemurs

kay doing Cylidical Shells and what not.

given y=sin(x^2)
from x=0..sqr(pi)
and rottated around the y-axis.

I use the forumla for intergration

V=2(pi)x F(x) d(x)

i get when i subsitute

2(pi)x Sin(x^2) d(x)
I know since 2(pi) is constan i pull it through the intergral.
Can I simplify : x Sin(x^2) in to something easier for integration.

2. Oct 1, 2006

StatusX

Substitution.

3. Oct 1, 2006

lemurs

just wanna make sure i did it right.. since it's been a while since i did substition.

for my question i woul have
u=x^2

du/dx=2x
du=2x dx
1/2(du) = x dx. which will fit into my orginal equation.

4. Oct 1, 2006

StatusX

That all looks right. Make sure to change the bounds as well.

5. Oct 1, 2006

lemurs

kay lost me there what you mean change the bounds?

6. Oct 1, 2006

StatusX

The integration goes from x=0 to x=sqrt(pi), so from u=0 to u=pi.

7. Oct 1, 2006

lemurs

ok.. don't understnad why i have to change my bounds... but iwill take your word for it.

8. Oct 1, 2006

StatusX

Good, that's the way math should be done. Seriously, what don't you understand? If you want to integrate from x=0 to x=sqrt(pi), and you have set u=x^2, then to integrate over the same region you need to go from u=0^2=0 to u=(sqrt(pi))^2=pi.