How to evaluate this double integral?

[Kuma]

Homework Statement

∫0 to 2 ∫x/4 to 1/2 (sin (pi*y²)) dy dx

Homework Equations

The Attempt at a Solution

I think I have to convert this to polar or do some sort of change of variable.

Although in polar y = r sin θ, so then you would have sin of a sin??

 

[blinktx411]

Try drawing the region and switching the order of integration, and this might allow you to use substitution rule hopefully, as I believe you will get something of the form $\int y*\sin(\pi y^2) dy$

 

[SammyS]

Homework Statement

∫0 to 2 ∫x/4 to 1/2 (sin (pi*y²)) dy dx

Homework Equations

The Attempt at a Solution

I think I have to convert this to polar or do some sort of change of variable.

Although in polar y = r sin θ, so then you would have sin of a sin??

Sketch the region (in the xy-plane) over which the integration is being done. Use this to switch the order of integration.