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The integral underset1overseteint{(x/e)^...

The integral `underset1overseteint{(x/e)^(2x)-(e/x)^x}log_exdx` is equal to

A

`3/2 - 1/e - 1/(2e^(2))`

B

`3/2 - e - 1/(2e^(2))`

C

`1/2 - e - 1/(e^(2))`

D

`-(1)/(2) + (1)/e - 1/(2e^(2))`

Text Solution

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The correct Answer is:
B
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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - II
  1. Let [] denote the greatest integet function then the value int0^1.5 x[...

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  2. The area of the region enclosed by the curve y=x, x=e,y=1/x and the po...

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  3. Find the area of the region bounded by the curve y^(2)=4x" and " x^(2)...

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  4. The area bounded between the parabolas x^(2)=(y)/(4) and x^(2)=9y and ...

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  5. If g(x) = int(0)^(x) cost dt, then g(x+pi) equals

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  6. Statement I The value of the integral int(pi//6)^(pi//3) (dx)/(1+sqrt...

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  7. The area (in square units) bounded by the curves y=sqrt(x),2y-x+3=0, x...

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  8. The integral int(0)^(pi)sqrt(1+4"sin"^(2)x/2-4"sin"x/2)dx is equals to...

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  9. The area of the region described by A={(x,y):x^(2)+y^(2)le1 and y^(2)l...

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  10. The integral int(2)^(4)(logx^(2))/(logx^(2)+log(36-12x+x^(2))) dx is e...

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  11. The area (in sq. units) of the region described by {x,y):y^(2)le2x and...

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  12. The area (in sq. units) of the region {(x,y):y^(2) le 2x and x^(2)...

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  13. lim(n -> oo) (((n+1)(n+2)(n+3).......2n) / n^(2n))^(1/n)is equal to

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  14. The area (in sq. units) of the region {(x,y):xge0,x+yle3,x^(2) le4y} a...

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  15. The Integral int(pi/4)^((3pi)/4)(dx)/(1+cosx) is equal to: ...

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  16. The value of int(-pi//2)^(pi//2)(sin^(2)x)/(1+2^(x))dx is

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  17. "Let "f(x)=cos x^(2),f(x)-sqrt(x), and alpha, beta (alphaltbeta) be th...

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  18. Let I=undersetaoversetbint(x^4-2x^2)dx. If is minimum, then the ordere...

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  19. The value of underset(-pi//2)overset(pi//2)intdx/([x]+[sinx]+4) where ...

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  20. The integral underset1overseteint{(x/e)^(2x)-(e/x)^x}logexdx is equal ...

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