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Sir please answer and specify the reason.

Sir please answer and specify the reason.

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Grade:12

1 Answers

Akshay
185 Points
6 years ago
∫ nxn-1/(1+x). dx = (∫ n.xn-1.dx)/(1+x) |01 – ∫ (∫n.xn-1.dx).d/dx(1/(1+x)), using recerse chain rule for integration.
∫ n.xn-1.dx = xand d/dx(1/(1+x)) = -1/(1+x)2, Put this above and take limits.
Lt ∫ nxn-1/(1+x). dx = Lt (1n/(1+1) – 0/(0+1))   +    Lt ∫ xn/(1+x)2 .dx,      -(1) 
Now Lt xn/(1+x)=0,
(1)- Lt ∫ nxn-1/(1+x). dx = ½
 

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