Question

Find the mass and center of mass of the lamina

Answer 1

the lamina is bounded by x^2 + y^2 = r^2, x is greater than or equal to zero, y is greater than or equal to 0

Answer 2

if p(x,y) = k(x^2 + y^2)

Answer 3

ok so for the double integral i know that the initial equation would be k(x^2 + y^2) but could i convert that to polar which is k(r^2) dr d(theta) and get the correct answer?

Answer 4

sorry i meant k(r^2) r dr d(theta)

Answer 5

so k r^3 dr d(theta)

Answer 6

\[\int\limits_{0}^{\pi/2}\int\limits_{0}^{r}kr^3 drd\]