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please solve this problem this problem from definite integration

please solve this problem this problem from definite integration

Question Image
Grade:12th pass

1 Answers

Phanindra
226 Points
3 years ago
Put (1-x) in place of x...there is property that..
Integral a to b x.dx = integral a to b (a+b-x)dx
So...u will get integral 0 to 1 log(1/1-x - 1) 
So..integral 0 to 1 log[(1-1+x)/1-x]
Integral 0 to 1 log (x/1-x)
Integral 0 to 1 logx  -  integral 0 to1 log(1-x)
Since log(a)/(b) = log(a) - log (b)...
So.. Int. 0 to 1 logx - int. 0 to 1 log(1-x)
Now use by parts formula...you will get the ans...
By the way don't forget to divide the second term with the coefficient of x ,that is" -1"....
u will definitely get the answer

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