IfIn=int0^1(1-x^5)^n dx ,t h e n(55)/7(I...

`IfI_n=int_0^1(1-x^5)^n dx ,t h e n(55)/7(I_(10))/(I_(11))i se q u a lto___`

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The correct Answer is:

8

`I_(11)=int_(0)^(1)ubrace((1-x^(5))^(2))_(I) . ubrace(1)_(II)dx`
`=(1-x^(5))^(11).x]_(0)^(1)+11int_(0)^(1)(1-x^(5))^(10)5x^(4).xdx`
`=0-55int_(0)^(1)(1-x^(5))^(10)(1-x^(5)-1)dx`
`=-55int_(0)^(1)(1-x^(5))^(11)dx+55I_(10)`
or `56I_(11)=55I_(10)`
or `(I_(10))/(I_(11))=56/55`

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