So as I see it, you've got yourself the integral
Is that correct? If so, I would definitely try to figure out the limits for the integrals next. What are those?
i'm sorry if this look messy and uni computers does not have latex installed, kindly please help to convert it to latex if possible and thank you in advance
Evaluate the following interral using geometrical interpretation
I= intergral( intergral( (a^2 -x^2 -y^2)^1/2 dxdy , where R is the disk given by
R = {(x,y):x^2+y^2 (smaller or equal than) a^2
the next step that i have done is to change it to intergral( intergral( (a^2 -r^2)^1/2 r.dr.d(digt)
after that i'm lost can any kind soul enlighten me on further steps?
and thank in advance to the guy if he manage to change this question to lastex format.
Yes, but since you've got the integral defined in terms of polar coordinates (definitely the way to go here), you'd like to be able to describe your domain in polar coordinates. If you could do that, then you should be able to read off the limits for your integral. So how would you describe your domain in polar coordinates?
Technically, it's a disk (the circle is the boundary). That is, because you have an inequality in the sets of my last post, you're including all the points on a circle of radius a, as well as all the points inside that circle.
So let's take our disk of radius a. What are the limits on r? What are the limits on theta?