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The value of
then ( m, n ) is
Given integral is
Put x = a + y
So, dx = dy
Since, in definite integrals, when we use substitution method, we have to change the limits too.
So,
When x = a, y = 0
and
When x = b, y = b - a
So, given integral reduced to
Now,
Again we use method of Substitution,
Put y = (b - a)x
So that dy = (b - a) dx
Now, again we have to change the limits.
When y = 0, x = 0
When y = b - a, x = 1
So, above integral reduced to
We know,
So, above integral can be rewritten as
We know,
So, above integral reduced to
We know,
So, using this identity, we have
So, it implies,
But it is given that,
So, on comparing we get
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