( 842, #15) Calculate the double integral

where R = { (x,y) : 1 <= x <= 2, 0 <= y <= 3}.

Solution:

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

Integrate_dydx(f,1,2, c, d);

f(x,y) = 2*y^2-3*x*y^3 c(x) = 0 d(x) = 3

int(f(x,y), y) = 2/3*y^3-3/4*x*y^4

int(f(x,y), y = c(x) .. d(x)) = 18-243/4*x

int( int(f(x,y), y = c(x) ..d(x)), x) = 18*x-243/8*x^2

int(int(f(x,y), y = c(x) ..d(x)), x = a .. b) = -585/8

visual check: average = -(585/8)/3.0 = -24.37500000

by: rjm