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# How do I integrate this?

I came across this problem today:

$$Verify\quad for\quad u(x,y)=e^{ x }sin(y)\quad the\quad mean\\ value\quad theorem\quad for\quad harmonic\quad functions\\ on\quad a\quad circle\quad C\quad of\quad radius\quad r=1,\quad with\quad its\\ centre\quad at\quad z=2+2i.$$

I tried to simplify it but I got stuck at the integral of $$cosh(e^{i\theta})$$. So my question is : how do I integrate $$cosh(e^{i\theta})$$?

I know that it is somehow related to $$Chi(e^{i\theta})$$, but I don't know how.

Note by Vishnu C
2 years, 1 month ago

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After some simplification I was able to verify, by integration, that it is true for the given function. But the question still stands: How is it related to $$Chi(e^{i\theta})$$? I was able to solve the case where the function had limits from 0 to 2*pi, i.e, I had to use some properties of definite integrals to simplify it. But is it possible to evaluate it with a general limit? · 2 years, 1 month ago

@Sandeep Bhardwaj Sir, @Raghav Vaidyanathan @Shashwat Shukla @Pranjal Jain @Abhishek Sinha Sir Please help him. Thanks a lot! @vishnu c · 2 years, 1 month ago