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

`I_1=int_0^(pi/2)ln(sinx)dx ,I_2=int_(-pi/4)^(pi/4)ln(sinx+cosx)dxdot` Then (a)`I_1=2I_2` (b) `I_2=2I_1` `I_1=4I_2` (d) `I_2=4I_1`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. f(x) is continuous function for all real values of x and satisfies int...

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  2. Prove that int0^1xe^xdx=1

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

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

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

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

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

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

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

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

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

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

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  13. If In=int0^1(dx)/((1+x^2)^n); n in N , then prove that 2nI(n+1)=2^(-n...

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

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

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

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

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

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

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