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!

1st FTOC

  1. Jan 27, 2009 #1
    Here's the question:

    integrate the function cos(sqrt(5t)) with lower bound: x and Upper bound: 6
     
  2. jcsd
  3. Jan 27, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Do a u substitution and then integrate by parts.
     
  4. Jan 27, 2009 #3
    but how?

    Should i integrate cos (sqrt(5t)) to 10/3 sin t ^3/2?
     
  5. Jan 27, 2009 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    That's completely wrong. If you differentiate (10/3)*sin(t^(3/2)) you don't anything like
    cos(sqrt(5t)). Try the substitution u^2=5t.
     
  6. Jan 27, 2009 #5
    would du=5/2u?

    because i did
    u^2 = 5t
    2udu = 5
    du = 5/2u
     
  7. Jan 27, 2009 #6

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    What you want to find is dt in terms of du. u^2=5t -> 2u*du=5*dt. dt=(2/5)*u*du.
     
  8. Jan 27, 2009 #7
    Thanks that is helpful, but i do not know how to apply it. Do you think you can walk me through the problem? I feel I have to see it before I can do it.
     
  9. Jan 27, 2009 #8

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You are doing fine. Use the substitution to write cos(sqrt(5t))*dt completely in terms of u. It's not that hard.
     
  10. Jan 27, 2009 #9
    i am just confused because the lower bound is x. I usually deal with the upper bound being x. Does this change the problem?

    would i get 2/5 u cos(sqrt(5t)) integrated from 6 to x ? do i change cos to sin?
     
  11. Jan 27, 2009 #10

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Uhhhhh. Your question is making me think that you didn't post the full problem. You want the DERIVATIVE of the integral, right? Not the integral.
     
  12. Jan 27, 2009 #11

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    If you actually want the derivative of that, pretend you know how to integrate it. So you have an F(t) such that F'(t)=cos(sqrt(5t)). By the FTOC, the integral is F(6)-F(x), right? What's the derivative of that? There is a difference between having x in the upper limit and the lower. Do you see what it is?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: 1st FTOC
  1. 1st derivative (Replies: 2)

  2. 1st ODE (Replies: 6)

  3. 1st order ODE (Replies: 1)

  4. 1st and 2nd Derivative (Replies: 4)

Loading...