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Evaluate: int(-pi/2)^(2pi)[cot^(-1)x]dx ...

Evaluate: `int_(-pi/2)^(2pi)[cot^(-1)x]dx` , where `[dot]` denotes the greatest integer function

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. int0^x[cost]dt ,w h e r ex in (2npi,2npi+pi/2),n in N ,and [dot] den...

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  2. Prove that int0^x[cot^(-1)x]dx ,w h e r e[dot] denotes the greatest in...

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  3. Evaluate: int(-pi/2)^(2pi)[cot^(-1)x]dx , where [dot] denotes the grea...

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  4. f(x) is continuous function for all real values of x and satisfies int...

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  5. Prove that int0^1xe^xdx=1

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  6. I1=int0^(pi/2)ln(sinx)dx ,I2=int(-pi/4)^(pi/4)ln(sinx+cosx)dxdot Then ...

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  7. Prove that int0^oo[n e^(-x)]dx=ln((n^n)/(n !)),w h e r en is a na...

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  8. For x in R and a continuous function f, let I1=int(sin^2t)^(1+cos^2t)...

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  9. Evaluate of each of the following integrals int(pi//6)^(pi//3)(sqrt...

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  10. Given a function f:[0,4]toR is differentiable ,then prove that for som...

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  11. Evaluate: int0^(pi/2)log((4+3sinx)/(4+3cosx))dx

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  12. The value of int0^1 4x^3 {d^2/(dx^2) (1 - x^2)^5 } dx is

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  13. Evaluate: int(-pi)^(3pi)log(s e c theta-t a ntheta)d theta

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  14. The value of the integral overset(1)underset(0)int e^(x^(2))dx lies in...

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  15. Let P(x) be a polynomial of least degree whose graph has three points ...

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  16. If In=int0^1(dx)/((1+x^2)^n); n in N , then prove that 2nI(n+1)=2^(-n...

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  17. If f(0)=1,f(2)=3,f^'(2)=5,then find the value of int0^1xf^('')(2x)d...

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  18. Ifinta^b(f(x))/(f(x)+f(a+b-x))dx=10 ,t h e n (a) b=22 ,a=2 (b) b=15 ...

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  19. Evaluate: int0^pi(dx)/(1+sinx)

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  20. if In=int0^(pi/4)tan^ntheta.d theta,then n in N,n(I(n-1)+I(n+1)) equal...

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