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Evaluate: int0^1x(1-x)^n dx...

Evaluate: `int_0^1x(1-x)^n dx`

Text Solution

Verified by Experts

Let,I= `int_0^1x(1-x)^n dx`
Let t=1−x⇒dt=−dx
When x=0⇒t=1
When x=1⇒t=0
I= `-int_1^0 (1-t)(t)^n dx`
I= `-int_1^0(t^n−t^(n+1))dt`
...
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