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If l(m,n)=intx^(m)cosnxdx, then prove th...

If `l_(m,n)=intx^(m)cosnxdx,` then prove that `l_(m,n)=(x^(m)sinnx)/(n)+(mx^(m-1)cosnx)/(n^(2))-(m(m-1))/(n^(2))l_(m-2,n)`

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Knowledge Check

  • If m, n in N , then l_(m n) = int_(0)^(1) x^(m) (1-x)^(n) dx is equal to

    A
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    B
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    C
    `(m!n!)/((m+n+1)!)`
    D
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  • Given that (L)/(M)+(M)/(N)+(N)/(L)=0 Then, (LN)/(M^(2))+(M^(2))/(LN)-(N^(3))/(L^(3))=?

    A
    1
    B
    `-2`
    C
    0
    D
    4

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