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

1. ## 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

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

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.

3. ## Re: Show that Int(1,infinity,sin(x^2)) converges

Thank you, that completes my proof.