Solving a Double Integral with k Converging to pi

[ashnicholls]

First attatchment is an integral I have been given.

Using different values of k I have to find out what value the integral converges too.

What I want to know is does this mean integrating the volume of circle with radius 1.

Shown in formula in the second attachment, I have also arranged it using polar coordinates.

And if that is right, I have found but only using mathcad that if k = 1/infinity the value converges to pi.

Is that right, because how I suppose to integrate the function shown using fractions to k, surely this is too complex to do by hand.

Cheers Ash

 

[ashnicholls]

And how do import pictures from mathcad into the post without having to make them attachments.

Cheers

 

[HallsofIvy]

A circle of radius 1 doesn't have a "volume"! What it means is that you are to integrate the given function over the interior of the circle.

And k can't "equal 1 over infinity" because infinity is not a number. Do you mean k= 0?

Yes, polar coordinates is the way to go here. You are aware, are you not, that $sin^2(\theta)+ cos^2(\theta)= 1$, so that x²+ y²= r²? That simplifies your integral a great deal!

 

[ashnicholls]

Yes sorry I meant area, not volume,

and yes i know it simplifies, i was just asking whether I had interpreted the problem correctly.

and yes by 1/infinity I did mean zero.

I was meaning as k gets smaller it converges to pi.

So is the function that i posted the right interpretation of the problem?

Cheers Ash