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Integrate: 1 / square root (x-a) (b-x)

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Solution:   we have , 

                   I=int frac1sqrt(x-a)(b-x)dx

               Put           (x-a)=z^2Rightarrow dx=2zdz

            \ \ herefore I=int frac2zzcdotsqrt(b-a)-z^2dz=2int frac1sqrt(b-a)-z^2dz\ \ Rightarrow I=2sin^-1fraczsqrtb-a+c=2sin^-1sqrtfracx-ab-a+c.              

 

Posted by

Deependra Verma

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