( 842, #11) Calculate the iterated integral

Solution:

f := (x,y)->sin(x):
c := x -> 0: d := x ->3:
Graph_dydx(f,0,Pi/4,c,d, 9);

Integrate_dydx(f,0,Pi/4,c,d);
f(x,y) = sin(x) c(x) = 0 d(x) = 3

int(f(x,y), y) = sin(x)*y

int(f(x,y), y = c(x) .. d(x)) = 3*sin(x)

int( int(f(x,y), y = c(x) ..d(x)), x) = -3*cos(x)

int(int(f(x,y), y = c(x) ..d(x)), x = a .. b) = -3/2*2^(1/2)+3

average value = (-3/2*2^(1/2)+3)/(3*Pi/4) = .3729232287

by: rjm