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

`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 ENGLISH-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 tang...

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

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  4. The area bounded by the curves y=cos x and y= sin x between the ordina...

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  5. For x epsilon(0,(5pi)/2), definite f(x)=int(0)^(x)sqrt(t) sin t dt. T...

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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 curve y=x, x=e,y=1/x and the po...

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  8. Find the area of the region bounded by the curve y^(2)=4x" and " x^(2)...

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

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  10. If g(x) = int(0)^(x) cost 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+sqrt...

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

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

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  14. The area of the region described by A={(x,y):x^(2)+y^(2)le1 and y^(2)l...

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  15. The integral int(2)^(4)(logx^(2))/(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(n -> oo) (((n+1)(n+2)(n+3).......2n) / n^(2n))^(1/n)is equal to

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  19. The area (in sq. units) of the region {(x,y):xge0,x+yle3,x^(2) le4y} a...

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  20. The Integral int(pi/4)^((3pi)/4)(dx)/(1+cosx) is equal to: ...

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