definite integral

Since , 0 < a < b < 1 ;

So , x ^{b - 1} > x ^{a - 1}

Hence , x ^{b - 1} - x ^{a - 1}1 - x > k1 - x ; where " k " is some finite constant which is less than ( x ^{b - 1} - x ^{a - 1} )

So , ∫ x ^{b - 1} - x ^{a - 1}1 - x dx > - k ln | 1 - x | ; By integrating .

If we put the limits now , then we see that the right side diverges .

Hene the integral must also diverge .

We can actually make it converge , but then we have to make " k " tend to zero .

In other words , we have to make " a " and " b " almost same .

But , then we have to have actual values of them .