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Consider the integral int0^(2pi)(dx)/(5-...

Consider the integral `int_0^(2pi)(dx)/(5-2cosx)` making the substitution `tan(x/2)=t ,` we have `I=int_0^(2pi)(dx)/(5-2cosx)` `=int_0^0(2dt)/((1+t^2)[5-2(1-t^2)/(1+t^2)])=0` The result is obviously wrong, since the integrand is positive and consequently the integral of this function cannot be equal to zero. Find the mistake.

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Evaluate: int0^pi(dx)/(1+sinx)

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  2. if In=int0^(pi/4)tan^ntheta.d theta,then n in N,n(I(n-1)+I(n+1)) equal...

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

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

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

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

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  7. Let f be a continuous function on [a ,b]dot Prove that there exists a ...

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  8. If f(x) is continuous for all real values of x , then sum(r=1)^nin...

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  9. F ind the value of int0^1logx dxdot

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  10. If An=int0^(pi/2)(sin(2n-1)x)/(sinx)dx ,Bn=int0^(pi/2)((sinn x)/(sinx)...

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  11. A continuous real function f satisfies f(2x)=3f(x)AAx in RdotIfint0^...

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  12. The value of int0^1(2x^2+3x+3)/((x+1)(x^2+2x+2))dx is

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  13. Evaluate: int(sin^(-1)x)/(1-x^2)^(3//2)dx

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  14. If f(x) is differentiable and int0^(t^2) x f(x) dx=2/5t^5, then f(4/(2...

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  15. Evaluate: int1^oo (e^(x+1)+e^(3-x))^(-1)dx

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  16. If f(x)=int(x^2)^(x^2+1)e^(-t^2)dt , then f(x) increases in

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  17. Estimate the absolute value of the integral int(10)^(19)(sinx)/(1+x^8)...

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  18. If I(m,n)=int0^1 t^m(1+t)^n.dt, then the expression for I(m,n) in term...

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  19. Prove that 4 lt= int1^3 sqrt(3+x^2) dx lt= 4sqrt(3)

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  20. If I1=int0^(pi//2)(cos^2x)/(1+cos^2x)dx , I2=int0^(pi//2)(sin^2x)/(1+s...

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