Compute Integrals: Integrate (z^3-6z^2+4)dz from -1+i to 1

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The discussion focuses on computing the integral of the function (z^3 - 6z^2 + 4)dz along any curve connecting the complex points -1+i and 1. Participants emphasize that the integral can be simplified by recognizing that the function is a polynomial, which allows for the use of its anti-derivative. The integral's value is independent of the path taken due to the properties of analytic functions in complex analysis.

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  • Basic concepts of path independence in integrals
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Integrate (z^3-6z^2+4)dz where the function is any curve joining -1+i to 1. Z is complex number
 
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Please post your progress so far so our helpers know exactly where you are stuck or what you may be doing wrong. (Nod)
 
I am trying to first separate them to integrate individual z^3dz, -6z^2dz and 4dz.

Line integral γ(t)= t*i+(1-t)*(-1-+i)
 
There is no need to find a parametric representation of the curve because the function you are integrating has an anti derivative , indeed it is a polynomial . By independence of the path , the integral only depends on the initial and final points .
 

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