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Homework Help: Integrate int (sin^2(t) + cos^2(t) -1)dt from e^x to e^(2x)

  1. Mar 19, 2008 #1
    1. The problem statement, all variables and given/known data

    Integrate from e^x to e^2x: (sin^2(t) + cos^2(t) -1)dt

    2. Relevant equations
    just standard integral equations


    3. The attempt at a solution

    I know how to do most of it, my only question is: is (sin^2(e^2x) + cos^2(e^x) -1) a special trig identity? or would i just solve it like a normal interation in parts problem?
     
  2. jcsd
  3. Mar 19, 2008 #2
    well it seems trivial to me... lol
    This question seems to be just tricky, nothing else.
     
  4. Mar 19, 2008 #3
    Aren't the sin and cos together adding to 1 the way you've written it, thus 1-1=0 ? You may want to double check you have it correct
     
  5. Mar 19, 2008 #4
    [tex]\int_{e^{x}}^{e^{2x}}(sin^{2}(t)+cos^{2}(t)-1)dt=\int_{e^{x}}^{e^{2x}}(1-1)dt=\int_{e^{x}}^{e^{2x}}(0)dt=?????[/tex]

    What does this equal to??
     
  6. Mar 19, 2008 #5
    ok, thanks guys lol. I feel dumb now
     
  7. Mar 19, 2008 #6
    Ok, integrate the following:

    [tex]\int_0^{ln(1)} sin(x)e^{-x^{2}}dx[/tex]

    This question was somewhere i dunno where though. Give a shot to it.

    HINT: THis is also tricky.
     
    Last edited: Mar 19, 2008
  8. Mar 19, 2008 #7


    Isnt that just equal to 1?
     
  9. Mar 19, 2008 #8
    Look at your limits of Integration

    From 0 to Ln(1)
     
  10. Mar 19, 2008 #9
    Why on earth do u think it is equal to 1?
     
  11. Mar 19, 2008 #10
    How did u change your display name?
     
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