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

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  2. For a positive integer n, let I (n) int (-pi)^(pi) ((pi)/(2) -|x|) cos...

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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. Find the limit, when n->oo,\ of\ [((n^3+1^3)(n^3+2^3)(n^3+3^3).........

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  5. Find the function f(x) if it satisfies the condition f(x)=x+int0^(...

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  6. If int0^1 sinx/(1+x)dx=K the the value of int(4pi-2)^(4pi)sin(x/2)/...

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  7. I=int(0)^(2)(3x^(2)-3x+1)cos(x^(3)-3x^(2)+4x-2)dx

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  8. Let u=int0^(pi//4)((cos x)/(sinx+cosx))^2dx\ a n d\ v=int0^(pi//4)(...

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  9. Evaluate (lim)(n->oo)n^2int(-1//n)^(1//n)(2010 sin x+2012cosx)|x|dxd...

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  10. Find value of following definite integrals: int(-pi/4)^(npi-pi/4)|s...

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  11. Evaluate: int0^2[x^2-x+1]dx ,w h e r e[dot] denotos the greatest inte...

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  12. Prove that: int0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx

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  13. Evaluate : int1^16tan^(- 1)sqrt(sqrt(x)-1)dx

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  14. Let f(x)=\ int1^xsqrt(2-t^2)dtdot Then the real roots of the equati...

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  15. Let T >0 be a fixed real number. Suppose f is continuous function su...

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  16. The tangent int(-1/2)^(1/2)([x]+ln((1+x)/(1-x)))\ dx equals, where [\ ...

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  17. int0^pisqrt((1-x)/(1+x))dx= (pi^)/2 (b) (pi^)/2-1 (c) (pi^)/2+1...

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  18. If f(x) is differentiable and int0^(t^2)xf(x)dx=2/5t^5, then f(4/(25))...

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  19. If y(x)=\ int(pi^2//16)^(x^2)(cos xdotcossqrt(theta))/(1+sin^2sqrt(the...

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  20. Find the value of int(-pi/3)^(pi/3)(pi+4x^3)/(2-cos(|x|pi/3))dx

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