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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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CENGAGE-DEFINITE INTEGRATION -Exercise (Numerical)
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  7. Let g(x) be differentiable on R and int(sint)^1x^2g(x)dx=(1-sint), wh...

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  8. If int0^oox^(2n+1)dote^(-xdx)=360 , then the value of n is

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  9. Let f(x) be a derivable function satisfying f(x)=int0^x e^tsin(x-t)dt...

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  10. Let f(x)=1/x^2 int0^x (4t^2-2f'(t))dt then find 9f'(4)

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  11. If the value of the definite integral int0^1^(2007)C7x^(2000)dot(1-x)^...

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  12. IfIn=int0^1(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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  15. The value of the definite integral int(2-1)^(sqrt(2)+1)(x^4+x^2+2)/((x...

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  16. Consider a real valued continuous function f such that f(x)=sinx + int...

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  18. Let y=f(x)=4x^(3)+2x-6, then the value of int(0)^(2)f(x)dx+int(0)^(30)...

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