complex analysis - integration

Ruth · #1 $Old$ June 7th, 2009, 03:55 AM

If having to integrate a conjugate do you multiply the function by the differential of the normal function or the differential of the conjugate?
e.g.integrate the real conjugate of t^3 -it. Thanking you in advance for any help.

HallsofIvy · #2 $Old$ June 7th, 2009, 03:09 PM

Quote:

Originally Posted by Ruth $View Post$

If having to integrate a conjugate do you multiply the function by the differential of the normal function or the differential of the conjugate?
e.g.integrate the real conjugate of t^3 -it. Thanking you in advance for any help.

Do you mean "integrate a conjugate" or "take the conjugate of the integral"?

If you mean "integrate a conjugate" then it is simply $\int \overline{f}(z)dz$ .

If you mean take "the conjugate of the integral" then $\overline{\int f(z)dz}= \int \overline{f}(z)d\overline{z}$ .

Ruth · #3 $Old$ June 8th, 2009, 12:44 PM

Thank you - it was the first I meant and I wasn't sure what to do - thought you had to integrate the function and then multiply by the derivative of the function according to cauchy's Integral theorem but didn'tknow if the derivtive was before or after finding the conjugate. How does everyone manage to type the mathematical stuff ?
Thanks again for your reply.