4 a thin triangular metal plate r is bounded by the lines y x x 1 andy

Question

4.A thin triangular metal plate (R) is bounded by the lines y = x,x = 1, andy = 0. The charge density of the plate is given by p(x, y) = e²² Coulombs per cm². (a) The total charge on the plate (in Coulombs) is given by the double integral \iint_{R} \rho(x, y) d A Find the total charge. \text { (b) Given that the average value of } f(x, y) \text { is given by } \frac{1}{A(R)} \iint_{R} \rho(x, y) d A \text {. } \bar{\tau}=\frac{1}{A(R)} \iint_{R} x d A \quad \bar{y}=\frac{1}{A(R)} \iint_{R} y d A Find the average charge density on the plate.