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

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

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CENGAGE ENGLISH-INTEGRALS-All Questions
  1. Let f:(0,oo)vec(0,oo) be a differentiable function satisfying, xint0^x...

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

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

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  4. If int0^1 (e^t dt)/(t+1)=a, then evaluate int(b-1)^b (e^t dt)/(t-b-1)

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

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

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

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

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  10. Iff(x)=int1^x(logt)/(1+t+t^2)dxAAxlt=1,t h e np rov et h a tf(x)=f(1/x...

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

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

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

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  14. 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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  15. f(x) is a continuous function for all real values of x and satisfies i...

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  16. If x=int0^y (dt)/sqrt(1+9t^2) and (d^2y)/(dx^2)=ay, then find a

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  17. The value of int(1/e)^(tanx)(tdt)/(1+t^2)+int(1/e)^(cotx)(dt)/(t(1+t^2...

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  18. Prove that: y=int(1/8)^(sin^2x)sin^(-1)sqrt(t)dt+int(1/8)^(cos^2x)cos^...

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  19. f(x)>0AAx in R and is bounded. If lim(n->oo)[int0^a(f(x)dx)/(f(x)+f(a...

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  20. Evaluate: int1^a xdota^(-[(log)a x])dx ,(a >1)dot

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