Integral notations..

Posted on 2006-04-11
Last Modified: 2008-03-03
What does it mean for the integral to have a lower limit, but no upper limit?

Is there a difference between having [for example] the lower limit directly below the integral sign, rather than slightly in front?

I've seen multiple integral signs next to each other, and there is what appears to be a single lower limit for _all_ of them (this 'lower limit' is centered along the bottom, of these signs). Does this just mean the 'nth' integral of y, with a lower limit of 'whatever' ?

I've also seen integral signs with circles on their 'belly' (I think I made that term up... I'm sure you know what I mean though). What does this mean? What does it mean for a group of integral signs to be 'sharing' one of these circles ?
...I think I read something about it meaning the magnitude of the result -- so, the positive value.. or something.. ?

Question by:InteractiveMind
    LVL 37

    Accepted Solution


    1) Sometimes, upper limit is taken as infinity, or in some other cases, it denotes the other variable's value
    2) No
    3) No, it means the integral is to be carried for each variable given, in the order the differentials (dx, dy etc) appear
    4) That is circular or contour integration, which means that the whole applicable values must be taken into account. It is generally used for area and volumes

    LVL 37

    Assisted Solution

    by:Harisha M G
    Probably, you are misunderstanding the meaning..

    Sometimes, the double integral over x and y is written as below.. (which means integral over the area)

    ⌡⌡ f(x,y) . dA

    and x, y and z as

    ⌡⌡⌡f(x,y,z) . dV

    which are same as

    ⌡⌡ f(x,y) . dx dy
    x y


    ⌡⌡⌡f(x,y,z) . dx dy dz
    x y z

    PS: Hope the characters get printed properly :)

    LVL 37

    Expert Comment

    by:Harisha M G
    LVL 84

    Assisted Solution

    LVL 37

    Expert Comment

    by:Harisha M G

    Featured Post

    IT, Stop Being Called Into Every Meeting

    Highfive is so simple that setting up every meeting room takes just minutes and every employee will be able to start or join a call from any room with ease. Never be called into a meeting just to get it started again. This is how video conferencing should work!

    Join & Write a Comment

    Foreword (May 2015) This web page has appeared at Google.  It's definitely worth considering! How to Know You are Making a Difference at EE In August, 2013, one …
    Have you ever thought of installing a power system that generates solar electricity to power your house? Some may say yes, while others may tell me no. But have you noticed that people around you are now considering installing such systems in their …
    Need more eyes on your posted question? Go ahead and follow the quick steps in this video to learn how to Request Attention to your question. *Log into your Experts Exchange account *Find the question you want to Request Attention for *Go to the e…
    Migrating to Microsoft Office 365 is becoming increasingly popular for organizations both large and small. If you have made the leap to Microsoft’s cloud platform, you know that you will need to create a corporate email signature for your Office 365…

    733 members asked questions and received personalized solutions in the past 7 days.

    Join the community of 500,000 technology professionals and ask your questions.

    Join & Ask a Question

    Need Help in Real-Time?

    Connect with top rated Experts

    21 Experts available now in Live!

    Get 1:1 Help Now