# Verify the equation of integration

I want to verify the the value of ##x_0## and ##y_0## of the given integral according to the formula of Mean Value of Harmonic function
$$\frac{1}{2\pi}\int_0^{2\pi} \cos(1+\cos t)\cosh(2+\sin t)\;dt$$

Mean Value of Harmonic function on a disk ##\Omega## given:
$$u(x_0,y_0)=\frac {1}{2\pi}\int_{\Omega}u[(x-x_0),(y-y_0)] d\Omega$$
$$\Rightarrow\;u[(x-x_0),(y-y_0)]=\cos(1+\cos t)\cosh(2+\sin t)$$
$$\Rightarrow\;(x-x_0)=1+\cos t,\;(y-y_0)=2+\sin t$$
Using Polar coordinates, ##x=r\cos t,\;y=r\sin t## where ##r=1## in this case.
$$(x-x_0)=1+\cos t\;\Rightarrow\; x_0=-1\;\hbox{ and }\;(y-y_0)=2+\sin t\;\Rightarrow\;y_0=-2$$

Am I correct?

Thanks

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