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The intensity pattern will only show peaks on the positions aligned with the slits, due to the collapse of the wavefunction to one of the states when measuring.
To get the value of the intensity, we can just take the sum of these two intensity peaks:
I_tot(x) = I_1 + I_2 = |A1|^2 + |A2^2
We see there is no interference term anymore in this expression.
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