(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider a lamina (two dimensional plate) with edges given by the lines y = sqrt(x) and

y = -x + 2x^(2), for which the density is given by P(x; y) = x.

(a) Define the domain of the lamina as the union of a Type 1 region and a Type 2 regions.

b) Calculate the mass.

Just looking for other peoples ideas for the domain, I have worked it out but am not sure if it is correct.

Thanks.

2. Relevant equations

3. The attempt at a solution

D = D(1) U D(2)

D(1) = 0≤ x ≤1/2 , -x+2x^(2)≤ y ≤0

D(2) = 0≤ y ≤1 , 1/4 (1 + sqrt(1+8y)≤ x ≤y^2

From this I got the mass equals 521/75.

I also tried calculating the mass from the domain just as a single typeI but got a mass of37/30.

Any help is appreciated. Thanks

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# Homework Help: Define the Domain of a lamina as union of Type 1 and Type 2 regions?

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