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Prove that int0^oo[n e^(-x)]dx=ln((n^n...

Prove that `int_0^oo[n e^(-x)]dx=ln((n^n)/(n !)),w h e r en` is a natural number greater than 1 and [.] denotes the greatest integer function..

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CENGAGE ENGLISH-INTEGRALS-All Questions
  1. Prove that int0^1xe^xdx=1

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

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

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

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

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

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

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

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

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

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

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  12. IfIn=int0^1(dx)/((1+x^2)^n),w h e r en in N , which of the following...

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

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  14. Ifinta^b(f(x))/(f(x)+f(a+b-x))dx=10 ,t h e n b=22 ,a=2 (b) b=15 ,1=-...

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

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  16. If I(n)=int(0)^(pi//4) tan^(n)x dx, (ngt1 is an integer ), then (a) I(...

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  17. Consider the integral int0^(2pi)(dx)/(5-2cosx) making the substitutio...

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  18. If f(x)=int0^x |t-1| dt, where 0 lt= x lt= 2 then (a) range of f(x) i...

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  19. If int0^1(e^(-x)dx)/(1+e^x)=(log)e(1+e)+k , then find the value of k.

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  20. The value of int0^oo (dx)/(1+x^4) is

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