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Find the value of integral (1/(sqrt(1+x)-sqrt(x)))dx limits 0 to 1

Find the value of integral (1/(sqrt(1+x)-sqrt(x)))dx limits 0 to 1

Grade:12th pass

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago
integral 1/sqrt(1+x)-sqrtx dx
=integral( sqrt(1+x)+sqrtx)/(sqrt(1+x)-sqrtx)(sqrt(1+x)+sqrtx) dx
=integral (sqrt(1+x)+sqrt(x))/1+x-x dx
=integral sqrt(1+x)+sqrt(x) dx
=2/3.(1+x)^3/2 +2/3.(x)^3/2
Now applying limit 0 to 1
2/3.[2^3/2-1^3/2]+2/3[1^3/2-0]
=2/3[(2)^3/2-1]+2/3
=2/3.(2)^3/2 Ans.
Thanks & Regards
Rinkoo gupta'
AskIItians faculty

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