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If lambda=int0^1(e^t)/(1+t), then int0^1...

If `lambda=int_0^1(e^t)/(1+t)`, then `int_0^1e^tlog_e(1+t)dt` is equal to

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`int_(0)^(1)e^(t)log_(e)(1+t)dt`
`=[e^(t)log_(e)(1+t)]_(0)^(1)-int_(0)^(1)1/(1+t) . e^(t)dt`
`=e log_(e)2-lamda`
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CENGAGE PUBLICATION-DEFINITE INTEGRATION -JEE ADVANCED
  1. If lambda=int0^1(e^t)/(1+t), then int0^1e^tloge(1+t)dt is equal to

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  2. Let f be a non-negative function defined on the interval [0,1]. If int...

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  3. The value of int0^1(x^4(1-x)^4)/(1+x^2)dxi s//a r e (22)/7-pi (b) 2/...

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  4. Let f be a real-valued function defined on the inverval (-1,1) such th...

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  5. The value of int(in2)^sqrt(in3) (xsinx^2)/(sinx^2+sin(In6-x^2)dx is

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  6. Let f:[-1,2]vec[0,oo) be a continuous function such that f(x)=f(1-x)fo...

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  7. Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-cons...

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  8. Let f : [0,2] rarr R be a function which is continuous on [0 , 2] and ...

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  9. int((pi)/4)^((pi)/2)(2cosecx)^17 dx

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  10. Let f prime(x)=(192x^3)/(2+sin^4 pix) for all x in RR with f(1/2)=0. I...

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  11. The value of int(-pi/2)^(pi/2) (x^2cosx)/(1+e^x) dx is equal to

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  12. If In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

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  13. about to only mathematics

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  14. Let S be the area of the region enclosed by y=e^(-x^(2)),y=0, x=0 and ...

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  15. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...

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  16. Let f:[a,b]rarr[1,infty) be a continuous function and lt g: RrarrR be ...

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  17. Let f:(0,oo)rarrRR be given by f(x)=oversetxunderset(1/x)inte^((t+1/...

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  18. The option(s) with the values of a and L that satisfy the following eq...

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  19. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2, pi/2). T...

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  20. find the period of sin(x/2)-cos(x/3) is

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  21. Let f: Rto(0,1) be a continuous function. Then, which of the following...

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