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If IK=int1^e(lnx)^kdx(k in I^+)dx(k in ...

If `I_K=int_1^e(lnx)^kdx(k in I^+)dx(k in I^+),` then find the value of `I_4dot`

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CENGAGE ENGLISH-INTEGRALS-All Questions
  1. IfI(m , n)=int0^(pi/2)sin^m xcos^n xdx , Then show that I(m , n)=(m-1...

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  2. Evaluate: int0^pi(xsin2xsin(pi/2cosx)/(2x-pi)dx

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  3. If IK=int1^e(lnx)^kdx(k in I^+)dx(k in I^+), then find the value of...

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  4. If int0^x {int0^u f(t) dt}du is equal to (a) int0^x (x-u) f(u) (b) ...

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  5. Prove that: In=int0^oox^(2n+1) e^ (-x^2) dx=(n !)/2,n in N.

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  6. The value of the integral underset(-1)overset(3 )int ("tan"^(1)(x)/(...

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  7. It is known that f(x) is an odd function in the interval [-p/2, p/2] ...

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  8. Evaluate: int(-1)^4f(x)dx=4a n dint2^4(3-f(x))dx=7, then find the val...

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  9. If int0^(pi/2)logsinthetad(theta)=k , then find the value of int0^(pi...

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  10. Evaluate: int0^(pi/2)|sinx-cosx|dx

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  11. Let f(x) is continuous and positive for x in [a , b],g(x) is continu...

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  12. Evaluate: int(-5)^5x^2[x+1/2]dx(w h e r e[dot] denotes the greatest i...

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  13. STATEMENT 1 : The value of int(-4)^(-5)sin(x^2-3)dx+int(-2)^(-1)sin(x^...

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  14. Evaluate: int0^(2pi)[sinx]dx ,where[dot] denotes the greatest inte...

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  15. STATEMENT 1 : The value of int0^1tan^(-1)((2x-1)/(1+x-x^2)) dx=0 STAT...

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  16. Evaluate: int0^oo[2e^(-x)]dx ,w h e r e[x] represents greatest int...

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  17. STATEMENT 1 : On the interval [(5pi)/4,(4pi)/3]dot the least value of ...

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  18. Evaluate: int0^(10pi)[tan^(-1)x]dx ,w h e r e[x] represents greatest ...

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  19. Consider the function f(x) satisfying the relation f(x+1)+f(x+7)=0AAx ...

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  20. Evaluate: int0^((5pi)/(12))[tanx]dx , where [dot] denotes the grea...

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