What are the limits of integration for evaluating a double integral?

[ilovemath88]

Homework Statement

Evaluate the following double integral:
∫ ∫ R sin (x/y) dA

where R is the region bounded by the y axis, y=pi and x=y^2

Homework Equations

as in problem statement

The Attempt at a Solution

Well I started this question by drawing the area to be evaluated. From this I chose my limits of integration, however I feel this may be where I am going wrong. I used ∫ (upper y=pi lower y=0) dy and ∫ (upper x=y^2 lower x=0) dx.
Im not sure if this is right first of all, and secondly, sin (x/y) is really tripping me up. This is because when I treat a variable as constant, where is it going. For example if I firstly evaluate sin (x/y) dy, I'm not sure of the result.

 

[tiny-tim]

Hi ilovemath88! Welcome to PF

(have an integral: ∫ and a pi: π and try using the X² and X₂ tags just above the Reply box )

Yes, your limits, ∫₀^π ∫₀^y2 are correct.

As you say, you have to treat one variable as a constant when you integrate wrt the other …

so which is easier to integrate first, sin(x/y)dx or sin(x/y)dy ?