Expressions are obtained for the integrals \[ I λ ( p ) = ∫ 0 π / 2 ( sin ⁡ λ θ sin ⁡ θ ) p d θ , J λ ( p ) = ∫ 0 π / 2 ( 1 − cos ⁡ λ θ sin ⁡ θ ) p d θ I_\lambda ^{(p)} = \int _0^{\pi /2}{\left ( {\frac {{\sin \lambda \theta }}{{\sin \theta }}} \right )^p}d\theta ,\quad J_\lambda ^{(p)} = \int _0^{\pi /2}{\left ( {\frac {{1 - \cos \lambda \theta }}{{\sin \theta }}} \right )^p}d\theta \] for arbitrary real values of " λ \lambda ", and p = 1 , 2 p = 1,2 .