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Question

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

A
2nm+1nm+1.l(m+1,n1)
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B
nm+1.l(m+1,n1)
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C
2nm+1+nm+1l.(m+1,n1)
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D
mn+1.l(m+1,n1)
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Solution

The correct option is C 2nm+1nm+1.l(m+1,n1)

Here, I(m,n)=10tm(1+t)ndt reduce into I(m+1,n1)

We have, I(m+1)(n1)=10tm+1(1+t)n1
(We apply integration by parts taking (1+t)n as first and tm as second function)

I(m,n)=[(1+t)n.tm+1m+1]1010n(1+t)(n1).tm+1m+1dt

I(m,n)=[(2)n.1(m+1)m+10]10n(1+t)(n1).tm+1m+1dt

I(m,n)=2nm+1nm+110(1+t)(n1).tm+1dt
I(m,n)=2nm+1nm+1.I(m+1,n1)

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