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{:(" " Lt),(n rarroo):} [(1^(2))/(n^(3)...

`{:(" " Lt),(n rarroo):} [(1^(2))/(n^(3)+1^(3))+(2^(2))/(n^(3)+2^(3))+......+(1)/(2n)]=`

A

`1/2 log 2`

B

`1/3 log 3`

C

`1/3 log 2`

D

`1/2 log 3`

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-DEFINITE INTEGRALS-PRACTICE EXERCISE
  1. Lt(ntooo)(1^(9)+2^(9)+3^(9)+.........+n^(9))/(n^(10))=

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  2. Lt(n rarr oo)[(1^(99)+2^(99)+3^(99)+...+n^(99))/(n^(100))]

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  3. {:(" " Lt),(n rarroo):} [(1^(2))/(n^(3)+1^(3))+(2^(2))/(n^(3)+2^(3))+...

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  4. Lt(ntooo)[(1)/(1+n^(2))+(2)/(1+n^(2))+.............+(n)/(1+n^(2))]

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  5. {:(" " Lt),(n rarroo):} pi/n (sin. pi/n + sin. (2pi)/(n)+sin. (3pi)/(...

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  6. {:(" " Lt),(n rarroo):} (pi)/(2n) (1+ cos. (pi)/(2n)+....+cos. ((n-1)...

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  7. Evaluate the following define integrals as limit of sums : lim(n rar...

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  8. Evaluate the limit. underset(n to 00)("lim") (sqrt(n+1)+sqrt(n+2)+…...

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  9. Lt(ntooo){(1)/(sqrt(n^(2)+1))+(1)/(sqrt(n^(2)+2^(2)))+.......+(1)/(sqr...

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  10. Evaluate the limit. underset(n to 00)("lim") (sqrt(n+1)+sqrt(n+2)+…...

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  11. Evaluate the following define integrals as limit of sums : lim(n rar...

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  12. int(r//6)^(pi//4)(dx)/(sin2x)=

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  13. int(1//pi)^(2//pi)(sin(1//x))/(x^(2))dx=

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  14. int(0)^(1)(4x^(3))/(sqrt(1-x^(8)))dx=

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  15. int(0)^(1) (1)/(sqrt(2+3x))dx=

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  16. int(0)^(1)(1-x)/(1+x)dx=

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  17. int(0)^(pi//2) (Cos x)/(1+Sin x) dx=

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  18. If f(x)int(0)^(k) (Cos x)/(1+Sin^(2)x)dx= pi/4 then K=

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  19. The solution of int(sqrt(2))^(x) (dt)/(tsqrt(t^(2)-1))=pi/12 is

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  20. int(0)^(1) (x^(5)dx)/(1+x^(4))=

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