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!

Integral of x^5secxdx

  1. Oct 3, 2011 #1
    Hi I m kinda stuck at this question.

    integral of x^5secxdx. I tried IBP n i couldnt carry on.
     
  2. jcsd
  3. Oct 3, 2011 #2
    Unfortunately, this integral is not expressible in terms of elementary functions.
     
  4. Oct 3, 2011 #3
    Ok my frene gave me the wrong info. int that interms of -1 to 1.
    I know the answer is 0 but why?
     
  5. Oct 3, 2011 #4
    Is the function [itex]f(x) = x^5 \sec{x}[/itex] even, odd or neither? When you have decided that, it should become clear as to why

    [itex]\int^{1}_{-1}{x^5 \sec{x}} dx = 0[/itex]
     
  6. Oct 3, 2011 #5
    I feel lost lol. How do i tell if it's even odd or neither?
     
  7. Oct 3, 2011 #6
    A function [itex]f[/itex] is even if [itex]f(x) = f(-x) \forall x \in domain[/itex]

    A function [itex]f[/itex] is odd if [itex]-f(x) = f(-x) \forall x \in domain[/itex]

    For your function, check [itex]f(x)[/itex] vs. [itex]f(-x)[/itex] vs. [itex]-f(x)[/itex].
     
    Last edited: Oct 3, 2011
  8. Oct 3, 2011 #7
    f(-x) = -x^5sec-x

    -f(x) = -(x^5secx)

    Is this the way?
     
  9. Oct 3, 2011 #8
    Sorry, I initially missed a negative sign in my last post.

    Yes, that's a way to check. And you know that sec(x) = 1/cos(x) and that cos(-x) = cos(x). Therefore, sec(-x) = sec(x). That implies that sec is an even function. However, (-x)^5 = -(x^5) implies that x^5 is an odd function. An even function times an odd function is itself an odd function.

    One property of an odd function, g(x), is that

    [itex]\int^{a}_{-a} g(x)dx = 0[/itex]
     
  10. Oct 3, 2011 #9
    On a related note, for an even function h(x),

    [itex]\int^{a}_{-a} h(x)dx = 2\int^{a}_{0} h(x)dx[/itex]

    If you graph some simple even and odd functions, you will see why this is the case.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Integral of x^5secxdx
  1. Integrate X²e^-x² (Replies: 11)

  2. Integral of x(e^x) (Replies: 1)

  3. Integral of x (Replies: 1)

Loading...