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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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To solve the problem, we need to evaluate the integral: \[ I = \int_0^1 e^t \log(1+t) \, dt \] We will use the method of integration by parts. The formula for integration by parts is: ...
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CENGAGE ENGLISH-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)\ dx is

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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 valued of int(sqrt(In2))^(sqrt(In3)) (x sinx^(2))/(sinx^(2)+sin(In...

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

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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]vecR be a function which is continuous on [0,2] and is diff...

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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. Evaluate: int(-pi//2)^(pi//2)(x^2cosx)/(1+e^x)dx

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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,a n dx=...

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  15. Find a for which lim(n->oo) (1^a+2^a+3^a+...+n^a)/((n+1)^(a-1)[(na+1)+...

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  16. Let f:[a,b]to[1,oo) be a continuous function and let g:RtoR be defined...

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  17. Let f:(0,oo) in R be given f(x)=overset(x)underset(1//x)int e^(t+(1)...

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  18. The option(s) with the values of aa n dL 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) . ...

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

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

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