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# Integral of a non-function?

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$$y=y^z+x^z$$

I wanna take the definite integral of that relation but I guess I am not sure of the notation or if it is even possible...and from x(or/and y?) = -1 to 1

Z is just some abratrary value greater than 1...

I do not want $$\int_{-1}^{1} \int_{-1}^{1} y^z+x^z dydx$$

It is a graph on $$R^2$$

So yeah.... wondering if there is some kind of trick or what... or if the domain of the integral is simply limited to functions

Guest Nov 24, 2017
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You can integrate them separately thus:

integral_(-1)^1 x^z dx = ((-1)^z + 1)/(z + 1) for Re(z)>-1

integral_(-1)^1 y^z dy = ((-1)^z + 1)/(z + 1) for Re(z)>-1

Guest Nov 24, 2017