Question Number 115071 by bemath last updated on 23/Sep/20
$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{cos}\:{x}}{\:\sqrt{\mathrm{1}−\mathrm{sin}\:{x}}}\:{dx}\:? \\ $$
Answered by Dwaipayan Shikari last updated on 23/Sep/20
$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{cosx}}{\:\sqrt{\mathrm{1}−{sinx}}}{dx} \\ $$$$−\int_{\mathrm{1}} ^{\mathrm{0}} \frac{{dt}}{\:\sqrt{{t}}}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dt}}{\:\sqrt{{t}}}=\left[\mathrm{2}\sqrt{{t}}\right]_{\mathrm{0}} ^{\mathrm{1}} =\mathrm{2} \\ $$