3.7 Improper Integrals

[STARTS AT 11:16]

Instructor: 57. The integral from negative 3 to infinity, of e to the negative x dx. State whether this converges or diverges. First thing, make that a limit. t is going to infinity. Integral of negative 3t, e to the negative x dx. OK. Well that integral can be done. That's going to be negative e to the negative x, evaluated from negative 3 to t. Can't forget our limit. All right. So that will be the limit as t goes to infinity of negative e to the negative t, minus plug our negative 3 in there, that will be negative e to the positive 3. So plus e to the 3. Right. Now as t goes to infinity, this is going to go to 0. And so this integral converges to e to the 3. Integral converges to e cubed, e the third power. 

[ENDS AT 12:30]