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what is the integration of square root of sin x a trignometric function

 
what is the integration of square root of sin x a trignometric function

Grade:12

1 Answers

BALAJI ANDALAMALA
askIITians Faculty 78 Points
5 years ago
\int \sqrt{sinx} dx = \int sinx.sin^{\frac{-1}{2}}x dx
Using the method of by parts ,\int sinx.sin^{\frac{-1}{2}}x dx = -cosx.sin^{\frac{-1}{2}}x + \int sin^{\frac{-1}{2}}x.cosx dx

= -cosx.sin^{\frac{-1}{2}}x + \frac{sin^{\frac{-1}{2}+1}x}{\frac{-1}{2}+1} + c
= -cosx.sin^{\frac{-1}{2}}x +2\sqrt{sinx} + c

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