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^{2}gives us the probability density of the wavefunction, Ψ. And when we integrate it, we get the probability of finding the particle at whichever location we desire, as set by the limits of the integration. But when we use the position operator, we have integrand Ψ*xΨ dx, which gives us the probability of finding the particle at a given place.

It seems to me as though, both of the above operations are doing the exact same thing. Then why do we have a position operator?