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

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To compute the integral of the function (z^3 - 6z^2 + 4)dz from -1+i to 1, the discussion emphasizes that the integral can be simplified by recognizing the function's polynomial nature, allowing for the use of its antiderivative. Participants suggest separating the integral into individual components: z^3dz, -6z^2dz, and 4dz. The path independence of the integral indicates that the result relies solely on the endpoints, negating the need for a specific parametric representation of the curve. The discussion encourages sharing progress to identify any issues encountered during the integration process. Ultimately, the integral's evaluation hinges on the properties of polynomials and their antiderivatives.
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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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