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Math Help - Si Ci Integral Notation

  1. #1
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    Si Ci Integral Notation

    I need some help figuring out what this notation means. I posted the problem and beneath it is some of the information I found about it





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  2. #2
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    Quote Originally Posted by qbkr21 View Post
    I need some help figuring out what this notation means. I posted the problem and beneath it is some of the information I found about it
    integral_{x=0 to pi/2} sin(x)cos(x)/[x+1] dx

    first combine the sin and cos to get:

    integral_{x=0 to pi/2} sin(x)cos(x)/[x+1] dx =

    ....................... integral_{x=0 to pi/2} sin(2x)/[2x+2] dx

    Now change the variable of integration to u = 2x+2, to get:

    integral_{x=0 to pi/2} sin(x)cos(x)/[x+1] dx =

    ....................... integral_{u=2 to pi+2} (1/2) sin(u-2)/u du

    ....................... integral_{u=2 to pi+2} (1/2) [sin(u)cos(2)-cos(u)sin(2)]/u du

    and the result should now follow from the definitions of the sin and cosin
    integrals Si and Ci.

    RonL

    added in explanation: you also need that for a sufficiently well behaved function:

    integral_{u=a to b} f(u) du = integral_{u=0 to b} f(u) du - integral_{u=0 to a} f(u) du
    Last edited by CaptainBlack; May 6th 2007 at 11:28 AM.
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