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: Finding definite integral (trigonometric)

  1. May 3, 2009 #1
    1. The problem statement, all variables and given/known data
    Hi guys ,, i have the following question (it's in the attachment) :
    Find m and M such that m <= x sin x <= M if 0 <=x <= pi. (Any reasonably good bounds will do,
    I am not asking for the best possible bounds.)
    Hence find bounds on the value of the integral[x sin(x),0 to pi]

    2. Relevant equations

    3. The attempt at a solution
    i have a formal solution (it's in the attachment) but the problem is i don't understand the question. Before i saw the question ,, i tried to solved it like this :
    since (0 <=x <= pi) then 0 <= x sin x <= 0 ( i solved for zero and pi) ,, and stopped there.
    can anyone tell me the problem in a way that i can understand ,, and in the answer it says "This is certainly not the best you could do, but it is definitely a bound" what does he mean ? is there many other ways to solve it ?? . (Thanks in advanced)

    Attached Files:

  2. jcsd
  3. May 4, 2009 #2
    If you graph the three functions y=x*sin(x), y=x, and y=-x using a window of xmin=0, xmax=30, ymin=-30, ymax=30, then I bet you will understand.

    If you're still puzzled, just graph the two functions y=abs(x*sin(x)) and y=x using the same window. Ask again if you are still confused after graphing.
  4. May 5, 2009 #3
    yep ,, got it :D ,, thanks very much mate,, but there is something else ,, i can get other bounds right ?? such as :
    0<= integral[x*sin(x),0 to pi]<= ((pi)^2)/2 ,, is this right ?
  5. May 5, 2009 #4
    Make it 0<= | integral[x*sin(x),0 to pi] | <= ((pi)^2)/2 (with absolute value) and I'll agree.

    Edited to add: Oh, never mind. x *sin(x) is positive there. Good job.
  6. May 5, 2009 #5
    lol ,, thanks :D
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook