Let be the lamina in the plane enclosed by the curve and by the lines ; , i. e. ,

y ; ; ].

Given that the density p(x; y) of the lamina is given by , calculate the mass of the

lamina.

the substitution u could be used or otherwise.

- Mar 4th 2011, 01:50 AMmaximus101Finding the mass of a lamina given the density and the description of the lamina
Let be the lamina in the plane enclosed by the curve and by the lines ; , i. e. ,

y ; ; ].

Given that the density p(x; y) of the lamina is given by , calculate the mass of the

lamina.

the substitution u could be used or otherwise. - Mar 4th 2011, 04:58 AMTKHunny
45 posts and not a hint of your own work?!

Here's a piece. You explain it to me and provide the other piece and the total evaluation.

- Mar 5th 2011, 04:20 AMHallsofIvy
But that suggested substitution does make for an interesting simplification. The Jacobian gives so the integrand becomes .

- Mar 5th 2011, 09:45 AMmaximus101
I think that integral you gave will give the density of the lamina, and we then have to find the surface area of it, then

however I'm not sure how you came to this integral and chose those limits, and do I have to apply to the inside integral and then to the result of the inside?

I drew the lamina and I think the upper and lower limit you chose for the inside uses the space between the straight lines and then on the outside integral I do not know how you chose but I know that the line meet the curve at - Mar 5th 2011, 09:49 AMmaximus101
once I make that substitution and the integrand becomes

how do I solve the integral and also do I have to change the limits,

I think I have to integrate the inside one first w.r.t du then the outer one w.r.t dv?

limits of the inside will change using and the outer one will use