How do i figure out if integrals are improper or not and how do i know which limit is undefined?

Improper integrals can take many forms. The first step when dealing with a potentially improper integral is to test the limits of the integral i.e. a and b. If these are at infinity/negative infinity, or the points are undefined at that value. You will have an improper integral. However, that ma not be the end of it. You will also have to quickly check that the curve is continuous over the integration, meaning that there are no asymptotes or undefined points midway through your integral. If there is such a point, the integral will need to be split into two - one integral for each side of the undefined point. Now we can actually solve our integral. Improper integrals can either be convergent or divergent - basically meaning whether the integral works or not. Convergent integrals will give us an answer whereas divergent ones will not. We should replace our undefined limit with t and create a limit. That limit will be t tends to x, where x is the undefined point. From there we perform our integration and solve.

HD
Answered by Hasha D. Further Mathematics tutor

3865 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

In simple harmonic motion, where would the object have the largest speed. If the angular velocity is 2 rad s^-1, and the amplitude is 1m, what is the largest speed obtained by the object?


Use induction to prove that for all positive integers n, f(n)=2^(3n+1)+3x5^(2n+1) is divisible by 17.


How do I determine whether a system of 3 linear equations is consistent or not?


Find the area of the surface generated when the curve with equation y=cosh(x) is rotated through 2 pi radians about the x axis, with 2<=x<=6


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences