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integrat sqrt(sinx) with limit 0 to pi/2.....................................

integrat sqrt(sinx) with limit 0 to pi/2.....................................
 

Grade:12th pass

1 Answers

Vikas TU
14149 Points
7 years ago
Apply By part integeration ---->
Let the first function be unity and second one root sinx.

integration of square root of sin x dx 
integration (sin x)^1/2 dx = [{(sin x)^3/2) / (3/2)}* cos x 
= [2cos x.sin x.(sin x)^1/2] / 3 
= [sin2x.(sin x)^1/2] / 3 

AAp;;y the limits

2nd method:
let sinx = t 
cos x dx= dt 
dx=dt/cosx 
= dt / (1-t^2)^1/2 
Required: integrate(sinx ^ 1/2 dx) 
integrate( [t^1/2 ]/[(1-t^2)^1/2 dt ) 
sorry ,I cant solve it by this method, 
BUT , I can give u the answer directly. 

ANSWER: 2/3[ ( sinx)^3/2]/cosx 
2/3 * (sinx)^3/2 * secx

 

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