Trig simplifycation and Intergration

[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) into something easier for integration.

 

[StatusX]

Substitution.

 

[lemurs]

just want to 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.

 

[StatusX]

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

 

[lemurs]

kay lost me there what you mean change the bounds?

 

[StatusX]

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

 

[lemurs]

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

 

[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.