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!

How do you differentiate & integrate e to the x?

  1. Sep 6, 2009 #1
    1.a Evaluate the following. Show all work.
    http://img90.imageshack.us/img90/289/problemu.png [Broken]
    1.b Differentiate.
    http://img293.imageshack.us/img293/1440/problem2.png [Broken]

    2. Relevant equations
    ƒ b-a f(x)-g(x)


    3. The attempt at a solution

    1.a.http://img511.imageshack.us/img511/1205/problemews.png [Broken]

    1.b.http://img512.imageshack.us/img512/4250/problem2ans.png [Broken]
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 6, 2009 #2
    e^2x does not integrate to 2e^2x because differentiation of 2e^2x is 4e^2x which is not equal to the e^2x.
     
  4. Sep 6, 2009 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Presumably, you know that [itex](e^x)'= e^x[/itex] and [itex]\int e^x dx= e^x+ C[/itex].

    To differentiate [itex]e^{2x}[/itex], use the chain rule, df/dx= (df/du)(du/dx), with u= 2x. Then [itex]f(u)= e^u[/itex] so [itex]df/du= e^u[/itex] and u= 2x so du/dx= 2.

    To integrate [itex]e^{2x}[/itex], use the "inverse" of the chain rule- substitution. Let u= 2x so du= 2dx or dx= (1/2)du.

    The one multiplies by 2, the other divides by 2.
     
  5. Sep 6, 2009 #4
    So [itex]e^2x[/itex] differentiated would become [itex]2e^2x[/itex]?
     
  6. Sep 6, 2009 #5

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    (I assume you mean e2x differentiated would become 2e2x?)

    Yes, that's right. :smile:

    (To see why, apply the chain rule with f(x) = ex and g(x) = 2x.)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How do you differentiate & integrate e to the x?
Loading...