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The integral int(0)^(pi)sqrt(1+4"sin"^2...

The integral `int_(0)^(pi)sqrt(1+4"sin"^2(x)/(2)-4"sin"(x)/(2))` dx is equal to

A

`4sqrt(3)-4`

B

`4sqrt(3)-4-(pi)/3`

C

`pi-4`

D

`(2pi)/3-4-sqrt(3)`

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Verified by Experts

The correct Answer is:
B
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TARGET PUBLICATION-DEFINITE INTEGRALS-COMPETITIVE THINKING
  1. int(0)^(100pi)|cosx|dx=…………………………..

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  2. int(0)^(pi//2) abs(sinx-cosx) dx=

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  3. The integral int(0)^(pi)sqrt(1+4"sin"^2(x)/(2)-4"sin"(x)/(2)) dx is e...

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  4. If I=int(1/ e)^e|logx|(dx)/(x^2) ,then I equals (A) 2 (B) 2...

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  5. int(0) ^(3) [x] dx= where [x] is greatest integer function

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  6. Let f(x) = x-[x], for every real number x, where [x] is integral part ...

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  7. The integral int0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest ...

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  8. The value of int0^9[sqrt(x)+2]dx, where [.] is the greatest integer fu...

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  9. If for all real numbers y ,[y] is the greatest integer less than or eq...

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  10. int(0)^((pi)/2)(x-[cosx])dx= (where [t]= greatest integer less or eq...

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  11. The value of int(1)^(a)[x]f'(x)dx, where agt1, and [x] denotes the gre...

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  12. If [x] denotes the greatest integer less than or equal to x then the v...

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  13. int- 2^2[x]dx

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  14. If [x] dentoes the greatest integer less than or equal to x, then the ...

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

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

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

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

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

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

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