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Show that : int0^1(logx)/((1+x))dx=-int0...

Show that : `int_0^1(logx)/((1+x))dx=-int_0^1(log(1+x))/x dx`

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CENGAGE ENGLISH-INTEGRALS-All Questions
  1. L e tA=int0^oo(logx)/(1+x^3)dx Then find the value of int0^oo(xlogx)/(...

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  2. Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0)=0,x in R , w...

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  3. Show that : int0^1(logx)/((1+x))dx=-int0^1(log(1+x))/x dx

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  4. The value of lim(n->oo) [tan(pi/(2n)) tan((2pi)/(2n))........tan((npi...

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  5. Evaluate: int0^pi(xsinx)/(1+cos^2x)\ dx

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  6. Match the statements/expression given in Column I with the values give...

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  7. If int0^t(bxcos4x-asin4x)/(x^2)=(asin4t)/t-1 where 0lttltpi/4, then th...

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  8. If I1=int0^pixf(sin^3x+cos^2x)dxa n d I2=int0^(pi/2)f(sin^3x+cos^2x)d...

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  9. int0^(pi/2)(sqrt(sinx))/(sqrt(sinx)+sqrt(cosx)) dx

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  10. If Un=int0^1x^n(2-x)^ndxa n dVn=int0^1x^n(1-x)^n dx ,n in N , and if ...

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  11. Find the value of int0^1 2x^3-3x^2-x+1 3dxdot

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  12. If int0^oox^(2n+1)dote^(-x^2)dx=360 , then the value of n is

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  13. Evaluate: int0^oo(dx)/(1+x^2)

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  14. Iflambda=int0^(pi/2)costhetaf(sintheta+cos^2theta)dtheta a n dI2=int0...

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  15. If f(a+b-x)=f(x), then prove that inta^b xf(x)dx=(a+b)/2inta^bf...

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  16. Let I1=int(-2)^2(x^6+3x^5+7x^4)/(x^4+2)dx and I2=int(-3)^1(2(x+1)^2+1...

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  17. Find the value of int0^(pi/2)sin2xdx

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  18. The value of int0^(pi/2)cos^2xdx

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  19. prove that |sint| is non-differentiable at t=pi.

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  20. Find the value of int0^1x(1-x)dx

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