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Question

If I(m,n)=10tm(1+t)ndt, then expression for I(m,n) in terms of I(m+1,n1) is

A
2nm+1nm+1I(m+1,n1)
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B
nm+1I(m+1,n1)
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C
2nm+1+nm+1I(m+1,n1)
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D
mm+1I(m+1,n1)
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Solution

The correct option is B 2nm+1nm+1I(m+1,n1)
Here, I(m,n)=10tm(1+t)ndt
[We apply integration by parts, taking (1+n) as first tm as second function]
I(m,n)=[(1+t)ntm+1m+1]1010n(1+t)n1tm+1m+1dt
=2nm+1nm+110(1+t)n1tm+1dt
Therefore, I(m,n)=2nm+1nm+1I(m+1,n1).

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