How do you solve integrals with e to a power?

[tiny-tim]

ah, you've calculated 4 times ∫₀^∞∫₀^∞ dxdy …

that's 4 times ∫₀^∞∫₀^π/2 drdθ, isn't it?

 

[opeth_35]

I think, I will not change the function when I calculate..

 

[tiny-tim]

sorry, you're misunderstanding …

the "4" is ok

it's the "2π" in your limit which was wrong, and needed to be changed to "π/2" (in red in my last post)

 

[opeth_35]

so, why did the function go from 0 to pi/2 ? :(

I don't understand that, on the other hand, the function could go from 0 to 2pi...

when can we see this kind of problems because I haven't figured out :(

 

[tiny-tim]

because your ∫∫ from 0 to ∞ was only over the first quadrant (x≥0, y≥0) …

that's 0 ≤ θ < π/2 ​

(if you'd kept to ∫∫ from -∞ to ∞, ie over all four quadrants, that would be 0 ≤ θ < 2π)

 

[opeth_35]

thank you for everything :) this explain was clear.. by the way, which profession do you have? just curious for me:) are u student or working university? :)

 

[tiny-tim]

i am a little goldfish,

and my job is swimming around all day, and keeping an eye on things

 

[opeth_35]

hahahaha:D, I think you don't want to talk about this.. okey , keep swimming:)