A word of caution.

[BigGlenntheHeavy]

In dealing with finding antiderivatives of integrals, first observe whether the integral is proper or improper as I didn't in klooless example below. Fortunately the improper integral converged, so no damage was done.

$\displaystyle For \ example, \ if \ we \ blindly \ evaluate \ \int_{-1}^{2} \frac{dx}{x^{3}}, \ we \ get \ \frac{3}{8}.$

This is wrong, as the integral is improper (infinite discontinuity at x = 0) and the integral actually diverges.

Just a thought for what it is worth dept., as I am as guilty as the next person.

 

[daon]

IIRC, this type of question is treated quite extensively in a "good" Calculus-2 class. Its too bad there are way too many "tips" one could give out in mathematics. Perhaps each section could have a sticky cooncerning common mistakes made in that particular area.