IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-94-011-6523-5_4.html
   My bibliography  Save this book chapter

Integral Calculus

In: Basic Mathematics for Biochemists

Author

Listed:
  • Athel Cornish-Bowden

    (University of Birmingham)

Abstract

Fig. 4.1 represents an arbitrary function y of x, and the area of the region bounded by the curve, the x-axis and the verticals x = x0 and x = x1 is designated A. What is the increase δA in this area if x1 is increased to x1 + δx?Apart from the small approximately triangular area that is shaded in the diagram, all of the increase in area is accounted for by the tall thin rectangle of height y1 and width δx,which has area y1 δx. In symbols, $$\delta A\simeq {{y}_{1}}\delta x$$ If x is made smaller, the small shaded triangle decreases rapidly in area, not only absolutely, but also in relation to the area of the rectangle. Consequently, the approximation embodied by the above equation is very accurate if δx is very small, and in the limit as δx approaches zero it becomes exact.

Suggested Citation

  • Athel Cornish-Bowden, 1981. "Integral Calculus," Springer Books, in: Basic Mathematics for Biochemists, chapter 4, pages 72-90, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-6523-5_4
    DOI: 10.1007/978-94-011-6523-5_4
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-94-011-6523-5_4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.