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Math Help - Contour Integrals

  1. #1
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    Contour Integrals

    How do I solve the following:

    I= Integral between 0 and 2pi [4dx/(2cosx+ 3sinx + 2i)]

    Thanks
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  2. #2
    Junior Member piglet's Avatar
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    Quote Originally Posted by Maths123 View Post
    How do I solve the following:

    I= Integral between 0 and 2pi [4dx/(2cosx+ 3sinx + 2i)]

    Thanks
    well what i'd normally do is use the following substitutions

    let  cosx = \frac{1}{2}(x + \frac{1}{x}) and  sinx = \frac{1}{2i}(x+\frac{1}{x})

    If you have any trouble from there on, just ask
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  3. #3
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    Right, I subbed that in.

    It's not working for me. I don't understand how you then go on to evaluate it further.

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  4. #4
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    I took 4 out, so got

    1/(x+(1/x)+(3/2i)x+ (3/2ix)+2i)

    Where do I go from there?
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  5. #5
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    Ok, so I get (2(17)^0.5)/2i+3

    Is that what you get? Where do I go from there?

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  6. #6
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    Is this integral to be evaluated on a closed path about the origin of the complex plane, or is this a line integral along the real x-axis?
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