Average (Expectation) Values (Particle in a Box)

and, given two eigenfunctions:

if a state is prepared which is one half of and one half , i.e., a linear combination with equal coëfficients, what is the expected energy ( ) of the resultant state?

Use `me' for the mass, `l' or `L' for the length of the box, and `h' for Planck's constant.
Answer is:

Query, is the above formula correct?