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I wonder if someone out there would help me understand the inner workings of MAPLE as indicated by the following: MAPLE has no trouble with int(sqrt(1-x^2)-x1,x=x1..sqrt(1-x1^2)); nor with this f1:=x->sqrt(1-x^2)-x1:int(f1(x),x=x1..sqrt(1-x1^2)); this one works too int(sqrt(r^2-x^2)-x1,x=x1..sqrt(r^2-x1^2)) assuming r>0,x1>0,r>x1; but for some reason not this one f2:=x->sqrt(r^2-x^2)-x1:int(f2(x),x=x1..sqrt(r^2-x1^2)) assuming r>0,x1>0,r>x1; Curiously, this works gg:=x->sqrt(r^2-x^2)-x1:int(gg(x),x):z:=unapply(%,x):z(sqrt(r^2-x1^2))-z(x1) The answer it gives looks different from the previous answer, but it evaluates the same when values of r and x1 are plugged in. So why the problem with the definite integral which used the previously defined function?
integral

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