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If int0^1(e^(-x)dx)/(1+e^x)=(log)e(1+e)+...

If `int_0^1(e^(-x)dx)/(1+e^x)=(log)_e(1+e)+k` , then find the value of k.

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CENGAGE PUBLICATION-INTEGRALS-All Questions
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  2. If f(x)=int0^x |t-1| dt, where 0 lt= x lt= 2 then (a) range of f(x) ...

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

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

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

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

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

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

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

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

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

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  19. Prove that int0^1sqrt((1+x)(1+x^3))\ dx cannot exceed sqrt((15)/8).

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

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