( 842, #13) Calculate the iterated integral

Solution:

f := (x,y)-> exp(2*x -y):
c := y ->0: d := y -> ln(5):
Graph_dxdy(f, 0, ln(2), c,d, 10);

Integrate_dxdy(f,0, ln(2), c, d);

f(x,y) = exp(2*x-y) c(y) = 0 d(y) = ln(5)

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

int(f(x,y), x = c(y) .. d(y)) = 12*exp(-y)

int( int(f(x,y), x = c(y) ..d(y)), x) = -12*exp(-y)

int(int(f(x,y), x = c(y) ..d(y)), y = a .. b) = 6

average = 6/(ln(2.0)*ln(5.0)) = 5.378380975

by: rjm