The orthogonality of normal functions of the longitudinal vibration of a bar is given by

a. \(\int_{0}^{l} U_{i}(x) U_{j}(x) d x=0\)

b. \(\int_{0}^{l}\left(U_{i}^{\prime} U_{j}-U_{j}^{\prime} U_{i}\right) d x=0\)

c. \(\int_{0}^{l}\left(U_{i}(x)+U_{j}(x)\right) d x=0\)