I think basically your mistake lies in your calculation of the modulus(magnitude) of -j which is 1 not -1.For use in the formula a*b=abcos#
where * means dot product
a/b mean the magnitudes(moduli) of a & b
hint
equate the arc sine to another variable e.g y.making it a sine fxn.e.g the arc sine of 0.5=30,while sine30=0.5.this will simplify the integral and further substitution will conclude it