In this lecture you will learn about Improper Integrals. Professor Murray will start you off with examples and formal notations of Horizontal Asymptotes and Vertical Asymptotes. You will also review the standard formula for Improper Integrals in order to master the many examples in this lecture.
is often useful to graph the function youre integrating to get a
general idea of its shape and whether it is positive or negative.
you usually cant eyeball the difference between finite and
infinite area. You need to do the integral and take the limit to be
that infinite positive and infinite negative areas do not cancel.
When we have both, we just say that the integral diverges.
you can make a substitution and convert an integral into one of the
It is worth memorizing the chart for which values of p make
these integrals converge or diverge. These integrals will also be
useful for examining infinite series in later sections.
out for hidden ambushes when the function is discontinuous or
its denominator is zero in the middle of your interval. In these
cases, split the integral up around the discontinuity and evaluate
improper integrals on both sides.
you get something that is difficult to integrate, you may need to
use the Comparison Test with an easier integral (often
A common comparison is to use the fact that −1 ≤ sin x ≤
1, and similarly for cos x.
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.