integrate ( 2x*pi ) cos( [pi/2] x^2 )

Medal for showing steps how to integrate!
I know this answer is 2pi (1/pi) sin( [pi/2]x^2 ), but I don't know how? Please help! Thank you :)

Question

integrate ( 2x*pi ) cos( [pi/2] x^2 )

Medal for showing steps how to integrate!
I know this answer is 2pi (1/pi) sin( [pi/2]x^2 ), but I don't know how? Please help! Thank you :)

dan815 · Answer

2*sin(x^2*pi/2)

geerky42 · Answer

Use U-substitution. Let $u = \dfrac{\pi}{2}x^2$, so $du = \pi x ~dx \rightarrow 2du = 2\pi x ~dx$

geerky42 · Answer

After this substitution, integral should be easy.

This helps? @student1988

anonymous · Answer

Thanks, I was trying integration but parts and couldn't come up with anything. But with U sub this is really easy. Thanks! :)

geerky42 · Answer

welcome