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
![∫_0 ^(π/2) ((cosx)/( (√(1−sinx))))dx −∫_1 ^0 (dt/( (√t)))=∫_0 ^1 (dt/( (√t)))=[2(√t)]_0 ^1 =2](https://www.tinkutara.com/question/Q115077.png)
$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{cosx}}{\:\sqrt{\mathrm{1}−{sinx}}}{dx} \\ $$$$−\int_{\mathrm{1}} ^{\mathrm{0}} \frac{{dt}}{\:\sqrt{{t}}}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dt}}{\:\sqrt{{t}}}=\left[\mathrm{2}\sqrt{{t}}\right]_{\mathrm{0}} ^{\mathrm{1}} =\mathrm{2} \\ $$