You get a bonus - 1 coin for daily activity. Now you have 1 coin

3.3.8. Improper integral

Lecture



Integrals with infinite limits and integrals of functions with infinite discontinuities on the integration interval are called improper integrals .

The improper integral of the function y = f ( x ) in the range from a to + ∞ is determined by the equality   3.3.8.  Improper integral .

If this limit exists and is finite, then the improper integral converges; if the limit does not exist (or is equal to infinity), then the improper integral diverges .

Similarly, the following improper integrals are calculated:

  3.3.8.  Improper integral

If the function y = f ( x ) has an infinite discontinuity at the point   3.3.8.  Improper integral and continuous for a ≤ x <c and c <x ≤ b , then   3.3.8.  Improper integral .

The improper integral of a function that has an infinite discontinuity on the integration interval is called convergent if both limits exist:   3.3.8.  Improper integral and divergent if at least one of these limits does not exist (or is equal to infinity).


Comments


To leave a comment
If you have any suggestion, idea, thanks or comment, feel free to write. We really value feedback and are glad to hear your opinion.
To reply

Mathematical analysis. Integral calculus

Terms: Mathematical analysis. Integral calculus