# Show that Int(1,infinity,sin(x^2)) converges

• July 12th 2011, 04:46 AM
solvj
Show that Int(1,infinity,sin(x^2)) converges
I need to show that integral of sin(x^2) from 1 to infinity converge

The only hint I have is "Let $y=x^2$". I did a change of variable at first and an integration by parts, but now I'm stuck. Does anyone can help me.

Thanks
• July 12th 2011, 05:45 AM
FernandoRevilla
Re: Show that Int(1,infinity,sin(x^2)) converges
Quote:

Originally Posted by solvj
The only hint I have is "Let $y=x^2$". I did a change of variable at first and an integration by parts, but now I'm stuck.

Good, now use $\left|\int_a^bf(x)\;dx\right|\leq \int_a^b|f(x)|\;dx$ and the fact that $\int_1^{+\infty}\dfrac{dt}{t^{3/2}}$ is convergent.
• July 12th 2011, 09:59 AM
solvj
Re: Show that Int(1,infinity,sin(x^2)) converges
Thank you, that completes my proof.