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The integral int0^pi sqrt(1 + 4 sin^2(x/...

The integral `int_0^pi sqrt(1 + 4 sin^2(x/2) - 4 sin (x/2)) dx` equals :

A

`4 sqrt3 - 4`

B

`4sqrt3 - 4 - pi/3`

C

`pi - 4`

D

`(2pi)/3 - 4 - 4sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
B
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PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
  1. Given that for each a in (0,1), underset(h rarr 0)(lim) inth^(1 - h)...

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  2. Match List - I with List - II

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  3. The integral int0^pi sqrt(1 + 4 sin^2(x/2) - 4 sin (x/2)) dx equals :

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  4. If I = int0^2 (e^x)^4 (x - alpha) dx = 0, then alpha lies in the inter...

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  5. Suppose M = int0^(pi/2) cosx/(x+2) dx , N = int0^(pi/4) sinxcosx/(x+1)...

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  6. Let f(x) = max{x + absx, x - [x]}, where [x] de notes the greatest int...

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  7. Let f(x) = {(int0^x abs(1 - t) dt , x gt 1),(x - 1/2 , x le 1):} Then

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  8. Statement - 1 : The value of the integral int(pi/6)^(pi/3) dx/(1 + s...

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  9. The value of the integral int-1^+1 { x^2013/(e^absx (x^2 + cos x)) +...

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  10. The value of I = int0^(pi/4) (tan^(n+1)x)dx + 1/2 int0^(pi/2) tan^(n-1...

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  11. The value of the integral int1^2 e^x (loge x + (x+1)/x)dx is

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  12. Let [a] denote the greatest integer which is less than or equal to a. ...

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  13. The value of the integral int (sin x - x cos x)/(x(x + sin x)) dx is e...

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  14. Let F(x) =int0^x (cos t)/(1 + t^2) dt , 0 le x le 2pi. Then

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  15. The value of the integral int(-pi/2)^(pi/2) (x^2 + In(pi + x)/(pi - x)...

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  16. If g(x)=int0^x cos^4t dt, then g(x + pi) equals

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  17. The value of the integral int(pi/6)^(pi/2) ((1 + sin 2x + cos 2x)/(sin...

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  18. The value of the integral int0^(pi/2) 1/(1 + (tanx)^101) dx is equal t...

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  19. The value of the integral int0^(pi/4) (sin x + cos x)/(3 + sin 2x) dx ...

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  20. The value of the integral int-2^2 (1 + 2 sin x) e^absx dx is equal to

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