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Evaluate the following definite integ...

Evaluate the following definite integrals: `int_0^1(e^(-x))/(1+e^x)dx`

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BANSAL-INTEGRALS-All Questions
  1. Evaluate the following definite integrals: int(1//e)^e|l\ n x|dx

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  2. Evaluate the following definite integral: int0^(pi//2)(sinx+cos x)dx

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  3. Evaluate the following definite integrals: int0^1(e^(-x))/(1+e^x)dx

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  4. Evaluate the following definite integrals: int0^(pi//4)(sinx+cosx)/...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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