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int(0)^(pi) [cotx]dx, where [*] denotes ...

`int_(0)^(pi) [cotx]dx`, where `[*]` denotes the greatest integer function, is equal to :

A

`1`

B

`-1`

C

`-(pi)/(2)`

D

`(pi)/(2)`

Text Solution

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The correct Answer is:
C
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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - II
  1. int(0)^(pi) [cotx]dx, where [*] denotes the greatest integer function,...

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  2. The area of the region bounded by the parabola (y-2)^(2) = x- 1, the t...

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  3. Let p(x) be a function defined on R such that p'(x) = p'(1-x) , for ...

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  4. The area bounded by the curves y=cosx and y=sinx between the ordinates...

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  5. For x in (0,(5pi)/(2)), defined f(x) = int(0)^(x) sqrt(t)sint dt. Then...

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  6. Let [] denote the greatest integet function then the value int0^1.5 x[...

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  7. The area of the region enclosed by the curvesv y=x,x=e,y=1/x and the p...

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  8. The area bounded by the curves y^2=4x and x^2=4y

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  9. The area bounded between the parabola x^(2)=y/4 and x^(2)=9y and the s...

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  10. If g(x) = int(0)^(x) cos dt, then g(x+pi) equals

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

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  12. The area (in square units) bounded by the curves y=sqrt(x),""2y-x+3=0 ...

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  13. The integral int(0)^(pi)sqrt(1+4sin^(2)'x/2-4sin'x/2)dx equals:

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  14. The area of the region described by A = {(x,y) : x^(2)+y^(2) le 1 and ...

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  15. The integral int(2)^(4) (logx^(3))/(logx^(2)+log(36-12x+x^(2)))dx is e...

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  16. The area (in sq units) of the region described by {(x,y):y^(2)le2x and...

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  17. The area (in sq. units) of the region {(x,y):y^(2) le 2x and x^(2)...

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  18. lim(nrarroo) (((n+1)(n+2)"........"3n)/(n^(2n)))^(1//n) is equal to :

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  19. The area ( in sq. units) of the region {(x,y) : x ge 0, x + y le 3, x...

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  20. The integral int(pi/4)^((3pi)/(4)) (dX)/(1+cosx) is equal to

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