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The integral int(1)^(e){(x/e)^(2x)-(e/x...

The integral `int_(1)^(e){(x/e)^(2x)-(e/x)^(x)}log_(e)` xdx 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))`

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The correct Answer is:
B
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RESONANCE-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 curvesv y=x,x=e,y=1/x and the p...

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  3. The area bounded by the curves y^2=4x and x^2=4y

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

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  5. If g(x) = int(0)^(x) cos 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+sq...

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

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

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  9. The area of the region described by A = {(x,y) : x^(2)+y^(2) le 1 and ...

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  10. The integral int(2)^(4) (logx^(3))/(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(nrarroo) (((n+1)(n+2)"........"3n)/(n^(2n)))^(1//n) is equal to :

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  14. The area ( in sq. units) of the region {(x,y) : x ge 0, x + y le 3, x...

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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 g(x) = cosx^(2), f(x) = sqrt(x), and alpha, beta (alpha lt beta)...

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  18. Let I=int(a)^(b)(x^(4)-2x^(2))dx. If I is minimum then the ordered pai...

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  19. The value of int(-pi//2)^(pi//2)(dx)/([x] + [ sin x] +4), where [t]...

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  20. The integral int(1)^(e){(x/e)^(2x)-(e/x)^(x)}log(e) xdx is equal to

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