Average Value

For a one dimensional problem (variable = x), obtain a formula for the average value of x, `<x>' of the described particle if the total range (domain) of x is a<=x<=b where a<b (a and b > 0), assuming the wave function over this domain is A/x<sup>1/2</sup> ( = A/sqrt(x)).
Use the single letters `A', `a', 'x' and `b' in your answer, `sin()' for the sine, `sqrt()' for the square root, and `log()' for the natural log. Multiplication signs must be indicated properly.
Answer is:

Query, is the above formula correct?