Posted by Bryant on Sunday, March 18, 2012 at 7:20pm.
Suppose R is the rectangle 1<=x<=4, y<=2 and evaluate the double integral ∫R∫f(x,y)dA, where f(x,y)= y/(1+3x^4)^(1/2).
I first decided to integrate with respect to y first (which I think I can choose to do)
I am a little confused at this part though cause i would get zero for my answer.
So instead i though about it as the integral from 0 to 2 plus the integral from 0 to 2 with respect to y for both and what i got left is
1/2∫8/(1+3x^4)^(1/2)dx
at this part i thought about using trigonometric substitution but i am hesitant to go on further just cause i don't know if i'm thinking about this problem the right way.

calculus  MathMate, Sunday, March 18, 2012 at 8:52pm
The given function is odd in y. No matter how you look at it, the integral for a rectangular region from a to +a will be zero.
If you split the integral into two, you should be adding
I(2,0) to I(0,2) which is still zero.
So the answer is zero, and a quick one if it is a bonus question in the exam.
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