0-pi-2-cos-3-x-1-cos-2-x-dx-

Question Number 149903 by bramlexs22 last updated on 08/Aug/21

Ω = \underset{0}{\int^{\frac{π}{2}}} \frac{\cos^{3} x}{\sqrt{1 - \cos^{2} x}} dx

Answered by Ar Brandon last updated on 08/Aug/21

Ω = \int_{0}^{\frac{π}{2}} \frac{\cos^{3} x}{\sqrt{1 - \cos^{2} x}} d x = \int_{0}^{\frac{π}{2}} \frac{1 - \sin^{2} x}{\sin x} \cos x d x

= \int_{0}^{1} (\frac{1}{u} - u) d u = {[\ln u - \frac{u^{2}}{2}]}_{0}^{1} = - \frac{1}{2} + \infty

divergent