BigGlenntheHeavy
Senior Member
- Joined
- Mar 8, 2009
- Messages
- 1,577
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.
\(\displaystyle For \ example, \ if \ we \ blindly \ evaluate \ \int_{-1}^{2} \frac{dx}{x^{3}}, \ we \ get \ \frac{3}{8}.\)
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.