1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Definite Integral

  1. Oct 24, 2012 #1
    Doing corrections on a test and I'm trying to solve this integral and I'm having quite a bit of trouble with it:

    __x
    Dx∫sqrt(5 + t^3) - e^t^2 dt
    __0

    I tried solving it by breaking it up into two integrals:

    x________________x
    ∫sqrt(5 + t^3) dt - ∫e^t^2 dt
    0________________0

    Then I tried using integration by parts, but that gets me things like du / 3t2 = dt, and dv / 2t = dt. What do I do?
     
  2. jcsd
  3. Oct 24, 2012 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You don't want to do the antidifferentiation. In fact, you can't, which is why you are having trouble. Differentiate the integral as a function of its upper limit using Leibnitz rule.
     
  4. Oct 24, 2012 #3

    Zondrina

    User Avatar
    Homework Helper

    Is the Dx in front the derivative operator? If so you need to use the fundamental theorem of calculus to solve this.
     
  5. Oct 24, 2012 #4
    Im only in Calculus II and I've never heard of such a thing. I did some Googling and I definitely don't know what that is.

    [Edit]Liebniz Rule isn't even mentioned in my textbook, and I'm almost certain it wasn't covered in class. Are you certain?[Edit]
     
  6. Oct 25, 2012 #5

    MarneMath

    User Avatar
    Education Advisor

    Leibniz rule is just a generalization of the fundamental theorem of Calculus. It's useful to know, even if it isn't covered in your book. Anyway, as everyone has pointed out FToC is what you need here. Whenever you see one variable in the limit of integration and a different one within the integral, your mind should jump to this. Also if you ever see e^t^2, you should know that you cannot integrate this, and if you are being asked to solve it, there must be some 'trick' to it.
     
  7. Oct 25, 2012 #6
    Alright then thanks. I guess I'ma watch some YouTube and go in for tutoring. No need to ask for a lesson here. I appreciate being pointed in the right direction : D Gracias.
     
  8. Oct 25, 2012 #7

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    That is odd. When I looked up 'Leibnitz Rule' in Google I got hundreds of hits.

    I would be willing to bet it WAS covered in class (although maybe not called that), because it is the very basis of doing integrals as "antiderivatives". It is absolutely fundamental, and any Calculus course worthy of the name will definitely cover it to some extent.

    RGV
     
  9. Oct 25, 2012 #8

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    I like to remember this as follows:


    Let F(x) be the anti-derivative of f(x).

    Then [itex]\displaystyle \int_0^x f(t)\,dt=F(x)-F(0)\ .[/itex]

    What is the derivative, with respect to x, of F(x) - F(0) ?

    It's given by [itex]\displaystyle \frac{d}{dx}(F(x)-F(0))=F'(x)-0=f(x)\ .[/itex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Definite Integral
  1. Definite Integral (Replies: 10)

  2. Definite integration (Replies: 4)

  3. Definite integral (Replies: 4)

  4. Definite integral (Replies: 6)

Loading...