We have already derived the integral formulae for the mass m,the moment My about the y-axis, and the moment Mx about the x-axis,of the region R where a lamina with density ?(x) resides in thexy-plane. The method we used was to:
-Slice R into n rectangles, where y = f(x) bounded R above and y= g(x) bounded R below, on [a, b].
-Compute the area, mass, and moments (about both the y-axis andthe x-axis), of the i th rectangle Ri .
-Take the Riemann sum limit to derive the integral formulae form, My, and Mx.
There are analogous integral formulae for m, My, and Mx, of R interms of y (in class we did it in terms of x). Indeed now assumethe region R is bounded to the right by x = f(y) and to the left byx = g(y) on [c, d] with density ?(y).
Adapt the method we did in class to derive the formulae for m,My, and Mx, as y-integrals.
You must label or define relevant variables and quantities, andat the end take the Riemann sum limit.
Note: Only by replacing x with y in the x-integralformulae does not yield the correct y-integralformulae.
please please focus on "note" and it is also for "yintegral"
I posted the question earlier but the answer was not theprofessor is looking for
