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IfI(m , n)=int0^1x^(m-1)(1-x)^(n-1)dx ,(...

`IfI(m , n)=int_0^1x^(m-1)(1-x)^(n-1)dx ,(m , n in I ,m ,ngeq0),t h e n` (a) `I(m , n)=int_0^oo(x^(m-1))/((1+x)^(m-n))dx` (b) `I(m , n)=int_0^oo(x^(m-1))/((1+x)^(m+n))dx` (c) `I(m , n)=int_0^oo(x^(n-1))/((1+x)^(m+n))dx` (d) `I(m , n)=int_0^oo(x^n)/((1+x)^(m+n))dx`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. The value of the definite integral, int0^(pi/2) (sin5x)/sinx dx is

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  2. The value of int0^pi (sin(n+1/2)x)/(sin (x/2)) dx is, n in I (a) pi/2 ...

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  3. IfI(m , n)=int0^1x^(m-1)(1-x)^(n-1)dx ,(m , n in I ,m ,ngeq0),t h e n...

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  4. If In=int0^(sqrt(3))(dx)/(1+x^n),(n=1,2,3. .), then find the value of ...

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  5. int0^1(tan^(-1)x)/x dx is equals to (a) int0^(pi/2)(sinx)/x dx (b)...

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  6. If int0^1(sint)/(1+t)dt=alpha, then the value of the integral int(4pi-...

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  7. L e tI1=int0^1(e^xdx)/(1+x) a n dI2=int0^1(x^2dx)/(e^(x^3)(2-x^3))dot ...

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  8. int(sintheta)^(costheta)f(xtantheta)dx(w h e r etheta!=(npi)/2,n in I...

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  9. Let g(x)=int0^x f(t).dt,where f is such that 1/2<=f(t)<=1 for t in [0,...

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  10. The value of int0^(pi/2) sin|2x-alpha|dx, where alpha in [0,pi], is (...

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  11. IfIn=int0^pie^x(sin"x")^("n")dx ,t h e n(I3)/(I1)"is equal to" (a) 3/...

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  12. int(-2)^0{(x+1)^3+2+(x+1)cos(x+1)dx is equal to (A) -4 (B) 0 (C) 4 ...

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  13. For any real number x, let [x] denote the largest integer less than or...

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  14. evaluate: int0^(pi/4)2tan^3xdx is

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  15. If f is continuous function and F(x)=int0^x((2t+3)*intt^2f(u)d u)dt , ...

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  16. Let f'(x)=(192x^3)/(2+sin^4pix) for all x in R with f(1/2)=0.If mleint...

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  17. If the value of lim(n rarr oo)(n^(-3/2)) sum(j=1)^(6n) sqrt(j) is equa...

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  18. If int0^xf(t) dt=x+intx^1 tf(t)dt, then the value of f(1)

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  19. If I=int0^((3pi)/4)[(1+x)sinx+(1-x)cosx]dx , then value of (sqrt(2)-1...

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  20. The value of int1^a[x]f^(prime)(x)dx ,where a >1, and [x] denotes the ...

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