# Trig simplifycation and Intergration

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.

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StatusX
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Substitution.

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.

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

kay lost me there what you mean change the bounds?

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

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

StatusX
Homework Helper
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.