= \frac{1}{2}I_{k-1} + \frac{1}{2}I_{k} + \frac{1}{2}[\frac{\cos^{k}(x)}{k}\sin(kx)]^{\theta}_{0} - \frac{1}{2}\displaystyle\int^{\t  heta}_0 cos^{k}(x)\cos(x) ] \, dx 