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l isum(n-gtoo)sum(r=1)^n1/(sqrt(4n^2-r^2...

`l isum_(n-gtoo)sum_(r=1)^n1/(sqrt(4n^2-r^2))`

A

`(pi)/(6)`

B

`(pi)/(4)`

C

`(pi)/(3)`

D

`(pi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`S=underset(nrarroo)(lim)sum_(r=0)^(n-1)(1)/(sqrt(4n^(2)-r^(2)))`
`rArr" "S=(1)/(n)underset(nrarroo)(lim)sum_(r=0)^(n-1)(1)/(sqrt(2^(2)-((r)/(n))^(2)))`
`rArr" "S=int_(0)^(1)(dx)/(sqrt(2^(2)-x^(2)))`
`rArr" "S=[sin^(-1).(x)/(2)]_(0)^(1)=sin^(-1).(1)/(2)-sin^(-1)`
`rArr" "S=(pi)/(6)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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  6. Evaluate int(0)^(pi)(x dx)/(1+cos alpha sin x),where 0lt alpha lt pi.

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  8. int(0)^(pi//2)(1)/((1+tanx))dx=?

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  10. The value of int (0)^(pi//2) log ("cosec "x) dx is

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  11. Which of the following is true ?

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  17. If f is a continous function, then

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  19. The value of int(-1)^(1) log ((x-1)/(x+1))dx is

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