evaluate the double integral by reversing the order of operation:

Question

anonymous · Answer

$$\int\limits_{0}^{\sqrt{\pi}}\int\limits_{y}^{\sqrt{\pi}}Cos(x ^{2})dxdy$$

anonymous · Answer

i keep getting 0

turingtest · Answer

$$y\le x\le\sqrt\pi$$$$0\le y\le\sqrt\pi$$|dw:1332356768545:dw|

turingtest · Answer

or is D on the other side...

anonymous · Answer

i don't know, all i was given is what i wrote

turingtest · Answer

No, I just need to figure it out...

anonymous · Answer

okay, can the answer to a double integral be a negative number?

turingtest · Answer

why not?

anonymous · Answer

idk, i thought it might be volume or something

turingtest · Answer

not, you are integrating a function over an area
if the function is negative over that area, then the integral will be negative
no magic there

phi · Answer

btw, 0 looks ok as an answer

turingtest · Answer

yeah, it is the region I drew with the D|dw:1332357396423:dw|
so$$y\le x\le\sqrt\pi$$$$0\le y\le\sqrt\pi$$implies$$x\le y\le\sqrt\pi$$$$0\le x\le\sqrt\pi$$so the integral is$$\large \int_{0}^{\sqrt\pi}\int_{x}^{\sqrt\pi}\cos(x^2)dydx$$um... did I mess up yet?