1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Evaluating Integrals Using Trigonometric Function Substitutions Question

  1. Aug 8, 2011 #1

    I just had this idea pop into my head... Can you use a trig sub with a reference triangle who has sides equal to zero? or more like a value close to zero such as dx or da or something?

    For example

    integral 1/sqrt(9+dx^2) (dx)^2

    would have a reference triangle were the hypotenuse is sqrt(9+dx^2)
    one of the legs would be 3
    the other leg would be dx

    you then could express dx/sqrt(9+dx^2) as either csc(theta) or sec(theta) depending on what leg you set 3 be equal to...

    integral 1/sqrt(9+dx^2) (dx)^2 = integral csc(theta) dx
    Last edited: Aug 8, 2011
  2. jcsd
  3. Aug 9, 2011 #2
    I really wounder what can be done if one sets the side of the length of the triangle to dx and try and make a sub some how if that makes any sense
  4. Aug 9, 2011 #3


    User Avatar
    Science Advisor

    This is an invalid integral. You cannot treat the "dx" as if it were a variable.
    An integral in x must be of the form [itex]\int f(x)dx[/itex].

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook