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!

FTC with a two-variable function

  1. Feb 12, 2014 #1
    https://en.wikipedia.org/wiki/Differentiation_under_the_integral_sign

    I don't understand where the last term comes from, the one that's an integral of a partial derivative. When I solve it using the FTC I get the same answer minus that term.

    If I differentiate first then integrate I get that term but then none of the others.
     
  2. jcsd
  3. Feb 12, 2014 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Work it out for yourself from first principles: if
    [tex] F(x) = \int_{a(x)}^{b(x)} f(t,x) \, dt,[/tex]
    then
    [tex] \frac{d}{dx} F(x) = \lim_{h \to 0} \frac{F(x+h) - F(x)}{h} [/tex]
    Work out the value of the numerator for small ##h > 0##; you will see that in general it involves several types of terms, and these give limits that are the terms in the final result you want.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: FTC with a two-variable function
Loading...