( 862, #1) Electric charge is distributed over the rectangle 0 <= x <= 2, 1 <= y <= 2 so that the charge density at (x, y) is sigma(x,y) = x² + 3 y² (measured in coulombs per square meter). Find the total charge of the rectangle.

The geometry:

sigma := (x,y) ->x^2 + 3*y^2:
c := x-> 1: d := x -> 2:
Graph_dydx(sigma, 0,2,c,d,10);

The integral is equal to 50/3:

Integrate_dydx(sigma,0,2,c,d);

echo: f(x,y) = x^2+3*y^2, c(x) = 1, d(x) = 2

int(f(x,y), y) = x^2*y+y^3

int(f(x,y), y = c(x) .. d(x)) = x^2+7

int( int(f(x,y), y = c(x) ..d(x)), x) = 1/3*x^3+7*x

int(int(f(x,y), y = c(x) ..d(x)), x = a .. b) = 50/3

by: nl