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If for all real numbers `y ,[y]` is the greatest integer less than or equal to `y ,` then the value of the integral `int_(pi//2)^(3pi//2)[2s in x]dx` is `-pi` b. 0 c. `pi//2` d. `pi//2`

A

`-pi`

B

`0`

C

`-(pi)/2`

D

`(pi)/2`

Text Solution

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The correct Answer is:
C
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TARGET PUBLICATION-DEFINITE INTEGRALS-COMPETITIVE THINKING
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  8. If [x] dentoes the greatest integer less than or equal to x, then the ...

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  9. int(0)^(11)((11-x)^(2))/(x^(2)+(11-x)^(2))dx=

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  10. int0^(pi/2) sqrt(sinx)/(sqrt(sinx)+sqrt(cosx))dx

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  11. int(0)^((pi)/2)(sin^(1000)x dx)/(sin^(1000)x+cos^(1000)x) is equal to

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  12. int(0)^((pi)/2)(tan^(7)x)/(cot^(7)x+tan^(7)x)dx is equal to

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  13. The value of the integral int(0)^(pi//2)(sqrt(cotx))/(sqrt(cotx)+sqrt(...

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  14. int(0) ^( pi//2) (root(n)(secx))/(root(n) (secx )+ root (n) ("cosec "x...

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  15. Evaluate the following : int(0)^(pi//2)(1)/(1+sqrt(tanx))dx

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  16. int(0)^((pi)/2)(dx)/(1+(tanx)^(sqrt(2018)))=

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  17. The value of int (0)^(pi//2) (2^(sinx))/(2^(sinx)+2^(cosx))dx is

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  18. int(0)^((pi)/2)(2008^(sinx))/(2008^(sinx)+2008^(cosx))dx=

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  19. int(0)^((pi)/2)(cos^(3)x)/(sinx+cosx)dx

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  20. int(0)^(pi//2) log (cotx ) dx=

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