Understanding Odd and Even Functions in Double Integrals

[Evilavatar2]

Homework Statement

Hi, I am not asking for solution for any problem as i already have the given solution for the problem. Instead, what i want clarify is what do they mean by the odd and even function and how do they get 0? Also, is there a need to change the order from dxdy to dydx?

 

[Simon Bridge]

What don't you understand?
http://math.stackexchange.com/quest...a-function-as-even-or-odd-help-in-integration
https://www.math.ucdavis.edu/~kouba/Math21BHWDIRECTORY/EvenOdd.pdf

 

[Evilavatar2]

But in the function, although both functions separate on its own are even, there is a negative sign in btween, if the left function is smaller than the right. In that case the result will be a odd function isn't it?
https://physicsforums-bernhardtmediall.netdna-ssl.com/data/attachments/97/97098-260351392c352c258bad5f10a0a53fe8.jpg

 

[PeroK]

But in the function, although both functions separate on its own are even, there is a negative sign in btween, if the left function is smaller than the right. In that case the result will be a odd function isn't it?
https://physicsforums-bernhardtmediall.netdna-ssl.com/data/attachments/97/97098-260351392c352c258bad5f10a0a53fe8.jpg

Is the function $x^2 - x^4$ even or odd or neither?

 

[mastermechanic]

If the function $x^2 - x^4$ even or odd or neither?

It's even.

If the all exponential numbers are even the function is even, if all are odd function is odd and if there are both odd and even exponential numbers the functions is neither odd nor even.

 

[PeroK]

It's even.

And the sum of any two even functions?

 

[mastermechanic]

And the sum of any two even functions?

I edited my answer read again

 

[PeroK]

It's even.

If the all exponential numbers are even the function is even, if all are odd function is odd and if there are both odd and even exponential numbers the functions is neither odd nor even.

If you want to generalise, you should be thinking about general even and odd functions.

Are you still confused about he one in your integral?

If so, try plugging in $x = 1$ and $x = -1$, say, and see how the function values compare.

 

[mastermechanic]

If you want to generalise, you should be thinking about general even and odd functions.

Are you still confused about he one in your integral?

If so, try plugging in $x = 1$ and $x = -1$, say, and see how the function values compare.

I'm not the one who confused about the even-odd functions :D You should say it to topic owner

 

[PeroK]

I'm not the one who confused about the even-odd functions :D You should say it to topic owner

Sorry! Although, I'm not sure why you jumped in and answered the question I asked the OP?

 

[mastermechanic]

Sorry! Although, I'm not sure why you jumped in and answered the question I asked the OP?

I thought you asked because you really don't know it that's why I answered

 

[Evilavatar2]

Sorry! Although, I'm not sure why you jumped in and answered the question I asked the OP?

Thanks a lot! i got it.