( 842, #5) Calculate the iterated integral

Solution:
f := (x,y)->x*y^(1/2):
c := y -> 0: d := y ->2:
Graph_dxdy(f,0,4,c,d, 12);

The double integral is equal to 32/3:

Integrate_dxdy(f,0,4,c,d);

f(x,y) = x*y^(1/2) c(y) = 0 d(y) = 2

int(f(x,y), x) = 1/2*x^2*y^(1/2)

int(f(x,y), x = c(y) .. d(y)) = 2*y^(1/2)

int( int(f(x,y), x = c(y) ..d(y)), x) = 4/3*y^(3/2)

int(int(f(x,y), x = c(y) ..d(y)), y = a .. b) = 32/3

visual check: average value = (32/3)(1/8) = 4/3

by: rjm