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About LinkBacksLetbe the lamina in the plane enclosed by the curve
and by the lines
;
, i. e. ,
 |)
 x)
y
;
;
].
Given that the density p(x; y) of the lamina is given by, calculate the mass of the
lamina.
the substitution ucould be used or otherwise.
Let
Given that the density p(x; y) of the lamina is given by
lamina.
the substitution u
I think that integral you gave will give the density of the lamina, and we then have to find the surface area of it, thenOriginally Posted by TKHunny
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.
however I'm not sure how you came to this integral and chose those limits, and do I have to applyto 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 chosebut I know that the line
meet the curve at
)
once I make that substitution and the integrand becomesBut that suggested substitution does make for an interesting simplification. The Jacobian givesso 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 usingand the outer one will use
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