How to solve this question? Here the options are given different but acc to dimension analysis, the trignometric values are dimenstionless

Dear student,

Here, do not assume x and a to be displacement or acceleration, respectively. Had this been the case, 1(dimensionless) could not be subtracted from the termon the right hand side.

All we can know from this term is that the dimensions of x and a are the same. Also, rightly said, the term insidemust be dimensionless. Hence the dimensions of the right hand side is that of.

The denominator of the integral term has dimensions of that of x or a. The numerator has that ofor, making the overall term have dimensions of x or a.

Since the dimensions of RHS and LHS must be same, the dimensions ofis equal to that of a. Hence n=1.