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F'(x)=sin((pi (e^x)) /2) and f(0)=1

  1. Apr 4, 2010 #1
    f'(x)=sin((pi (e^x)) /2) and f(0)=1 then f(2)= ?

    so i integrate and get -(1/((pi/2)*e^x)) cos((pi (e^x)) /2)+ 1=1

    when i plug two into that i dont get any of the answers listed

    a)-1.819
    b) -.843
    c.) -.819
    d) .157
    e) 1.157
     
  2. jcsd
  3. Apr 5, 2010 #2

    CompuChip

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    Re: Integration

    Are you supposed to do this analytically? Because I can't really find a primitive function for sin(pi e^x / 2). I can do the integration numerically though, and get one of the listed answers.
     
  4. Apr 5, 2010 #3
    Re: Integration

    What he said. Your "integrate" is incorrect. Instead of finding an exact formula, can you tell by looking at the sign and approximate size of the RHS that all but one of the answers is ruled out?
     
  5. Apr 5, 2010 #4
    Re: Integration

    If you have a calculator (which I can assume by the answer choices), try Euler's method.
     
  6. Apr 8, 2010 #5

    dextercioby

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    Re: Integration

    Use the Taylor series around 0 (aka MacLaurin), mate.

    http://mathworld.wolfram.com/TaylorSeries.html

    Up to third derivative I get

    1+2-(pi^2 / 3) approx = -0.290.

    Then u compute up to 5th derivative and see what you get.
     
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