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Let f(x) = 1/x ln(x/e^x) then its primit...

Let `f(x) = 1/x ln(x/e^x)` then its primitive w.r.t x is

A

`(1)/(2)e^(x)-lnx+C`

B

`(1)/(2)lnx-e^(x)+C`

C

`(1)/(2)ln^(2)x-x+C`

D

`(e^(x))/(2x)+C`

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FIITJEE-DEFINITE INTEGRAL -ASSIGNMENT PROBLEMS (OBJECTIVE) (LEVEL-I)
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  2. int(-1)^(1)[tan^(-1){sin(cos^(-1)x)}+cot^(-1){cos(sin^(-1)x)}dx=

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  3. int- 8^8(sin^(93)x+x^(295))\ dx

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  4. Let I=int0^1(sin)/(sqrt(x))dx"and"J=int0^1(cosx)/(sqrt(x))dx Then w...

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  5. int0^100 {sqrtx} dx (where {x) is fractional part of x ) =

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  6. int(a)^(b)(f(x))/(f(x)+f(a+b-x))dx=

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  7. If bgta, then int(a)^(b)(dx)/(sqrt((x-a)(b-x))) is equal to

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  8. inta^bsqrt((x-a)(b-x)) dx , a > b

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  9. Let f(x)=int(1)^(x)t(t^(2)-3t+2)dt,1lexle4. Then the range of f (x) is

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  10. Suppose g(x) satisfies g(x)=x+int(0)^(1)(xy^(2)+yx^(2))g(y)dy, then g(...

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  11. For x epsilonR, and a continuous function f let I(1)=int(sin^(2)t)^(1+...

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  12. If overset(4)underset(-1)int f(x)=4 and overset(4)underset(2)int (3-f(...

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  13. If f(x)=f(a+b-x), then overset(b)underset(a)int xf(x)dx is equal to

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  14. If f(x)=int((1)/(x))^(sqrt(x))cost^(2)dt(xgt0)" then "(df(x))/(dx) is

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  15. Let f(x) = 1/x ln(x/e^x) then its primitive w.r.t x is

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  16. The greatest value of f(x)=int1^x|t|\ dt on the interval [-1/2,1/2] :

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  17. int0^pi dx/(1-2acosx+a^2), alt1 is equal to (A) (pialog2)/4 (B) (4pi)/...

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  18. If =underset(1)overset(e)int (logx)^(n) dx, "then"I(n)+nI(n-1) is equa...

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  19. int(0)^(pi//2)(dx)/(1+a^(2)sin^(2)x) has the value

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  20. Statement 1: int(0)^(10)(2^(x))/(2^([x]))dx=(10)/(ln2) (where [.] deno...

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