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Evaluate : int_(0)^(1) (x)/(sq...

# Evaluate : int_(0)^(1) (x)/(sqrt(1+x^(2)))dx

Updated On: 17-04-2022

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Text Solution

Solution :
Let 1+x^(2) =t <br> rArr " "2x dx =dt " "rArr " "x dx =(dt)/(2) <br> At x=0 , " "t=1 +0=1 <br> Atx=1, " " t=1+1=2 <br> "Now " int_(0)^(1) (x)/(sqrt(1+x^(2)))dx <br> =int_(1)^(2)(dt)/(2sqrt(t)) =1/2 int_(1)^(2) t^(-1//2) dt <br>  =1/2 [(t^(1//2))/(1//2)]_(1)^(2) =(sqrt(2)-1).

Answer

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