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Good day , i have an issue with the derivation of the mutual inductance of coil inside solenoid formula

I1 is an alternating current which means that B is varying, and we know that the Flux 21 is equal to the integral of the dot product of B and A2 but as B is varying

Maybe there is something missing in my logic and any help would be highly appreciated, thanks!!!

I1 is an alternating current which means that B is varying, and we know that the Flux 21 is equal to the integral of the dot product of B and A2 but as B is varying

**take it out of the integral and use the form used in the pic (the formula encercled in red).**__we CAN NOT__Maybe there is something missing in my logic and any help would be highly appreciated, thanks!!!