Where is the path difference.

The net amplitude at P will be sum of effect due to all the elements ds and can be obtained by integrating dE_s from s=-d/2 to d/2 where d is the width of the slit. In doing so, we can first sum the amplitude produced by the symmetrically placed elements ds and then integrate it from s=0 to d/2. The contribution due to a pair of symmetrically placed element ds is

                       

                   

Using the trigonomerical identity We have