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Evaluate lim(xrarr0)(x-int0^(x) cost^2dt...

Evaluate `lim_(xrarr0)(x-int_0^(x) cost^2dt)/(x^3-6x)`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. The integral int(-1/2)^(1/2) ([x]+1n((1+x)/(1-x)))dx is equal to (wher...

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  2. Evaluate: int0^(e-1)(e^((x^2+2x-1)/2))/(x+1)dx+int1^e xlogx e^(x^(2-2)...

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  3. Evaluate lim(xrarr0)(x-int0^(x) cost^2dt)/(x^3-6x)

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  4. The value of 2^(2010)(int0 ^1x^(1004)(1-x)^(1004)dx)/(int0^1x^(1004)(...

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  5. If int(0)^(1)(e^(t))/(1+t)dt=a then find the value of int(0)^(1)(e^(t)...

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  6. If f(x)=x+int0^1t(x+t)f(t)dt ,then the value of 23/2f(0) is equal...

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  7. Let f:(0,oo)to(0,oo) be a differentiable function satisfying, int0^x(1...

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  8. If f(x)a n dg(x) are continuous functions, then int(1nlambda)^(1n1/lam...

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  9. The value of int-pi^pi cos^2x/[1+a^x]dx, a > 0 is

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  10. If b=int(0)^(1) (e^(t))/(t+1)dt, then int(a-1)^(a) (e^(-t))/(t-a-1) is

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  11. If f(x)=x+sinx , then find the value of intpi^(2pi)f^(-1)(x)dx.

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  12. Let F(x)=intx^[x^2+pi/6](2cos^2t)dt for all x in R and f:[0,1/2] -> [0...

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  13. If f(x) is a function satisfying f(1/x)+x^2f(x)=0 for all nonzero x , ...

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  14. I1=int0^(pi/2)(sinx-cosx)/(1+sinxcosx)dx ,I2=int0^(2pi)cos^6xdx ,I3=in...

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  15. The value of the integral int(e^(-1))^(e^2)|((log)e x)/x| dx is (A)...

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  16. f(x)=int1^xlogt/(1+t+t^2)dt (xge1) then prove that f(x) =f(1/x)

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  17. If f(x) = int0^pi (t sint dt) / (sqrt(1+tan^2xsin^2t)) for 0 < x < pi/...

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  18. Evaluate: int(sqrt(2)-1)^(sqrt(2)+1)((x^2-1))/((x^2+1)^2)dx

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  19. int0^x(2^t)/(2^([t]))dt ,w h e r e[dot] denotes the greatest integer f...

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  20. Ify=int0^xf(t)sin{k(x-t)}dt ,t h e np rov et h a t(d^2y)/(dx^2)+k^2y=k...

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