Things not to do. (updated 10/27/16)

OK. I'm grading the exam and not pulling my hair out, but only because I don't have enough hair to do that. So, purely for your edification, I thought I would make a rogue's gallery of things not to do.

1) DO NOT REVERSE THE ORDER OF AN ITERATED INTEGRAL BY SIMPLY REWRITING THE INTEGRALS IN THE REVERSE ORDER.  (Limits of integration that are functions can never, ever,wind up in the outside integral.  

2) Do not simply change replace the variables in the limits of integration for the inside integral without changing the functional form.  This will never work either.

3) The antiderivative of a function is NOT the same as the derivative.  For instance 

∫ 1/(1+x^5)dx≠5x^4(1+x^5)^-2

4) 1/(a+b)≠1/a + 1/b.  NEVER, EVER.

5) Do not write a negative answer for an integral when the integrand is strictly non-negative on the domain of integration.

6) When you are computing the value of an iterated integral, be sure you compute the antiderivative of the inside integral with respect to the inside variable,  for instance
∫_a^b∫_f1(x)^f2(x) x dy dx = ∫_a^b x y |_y=f1(x)^y=f2(x) dx = ∫_a^b x f2(x)-x f1(x) dx

but
∫_a^b∫_f1(x)^f2(x) x dy dx ≠ ∫_a^b 1/2 x^2 |_y=f1(x)^y=f2(x) dx = ∫_a^b 1/2(f2(x)^2-f1(x)^2) dx