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The area (in sq units) of the region bou...

The area (in sq units) of the region bounded by the curves `y = e^(x)`, `y = log_(e)` x and lines x = 1, x = 2 is

A

`(e-1)^(2)`

B

`e^(2)-e+1`

C

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

D

`e^(2)+e-2log_(e)2`

Text Solution

Verified by Experts

The correct Answer is:
C
Required area, `A=int_(1)^(2)(e^(x)-log_(e)x)dx`

`=[e^(x)]_(1)^(2)-[xlog_(e)x-int1dx]_(1)^(2)`
`=e^(2)-e-[xlog_(e)x-x]_(1)^(2)`
`=e^(2)-e-[2log_(e)2-2-(0-1)]`
`=e^(2)-e-2log_(e)2+1`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-APPLICATIONS OF DEFINITE INTEGRALS -Exercise 2
  1. For 0 lt= x lt= pi, the area bounded by y = x and y = x + sin x, is

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  2. If the area above the x-axis, bounded by the curves y = 2^(kx) and x =...

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

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  4. The area in the first quadrant between x^2+y^2=pi^2 and y=sinx is

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  5. The area bounded by the curves y=sqrtx, 2y-x+3=0, X-axis and lying in ...

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  6. The area bounded by y = |sin x|, X-axis and the line |x|=pi is

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  7. Find the area bounded by the x-axis, part of the curve y=(1-8/(x^2)) ,...

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  8. The area bounded by the graph of y=f(x), f(x) gt0 on [0,a] and x-axis ...

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  9. The line x = (pi)/(4) divides the area of the region bounded by y = si...

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  10. The area bounded by the curve y=x|x|, x-axis and the ordinates x=1,x=-...

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  11. The area (in sq units) of the region bounded by the curves y = e^(x), ...

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

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  13. The larger of the area bounded by y = cosx, y = x + 1 and y = 0 is

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  14. The parabola y^2 = 2x divides the circle x^2 + y^2 = 8 in two parts. T...

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  15. The figure shows a DeltaAOB and the parabola y = x^(2). The ratio of t...

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  16. The area bounded by y = sin^(-1)x,x=(1)/(sqrt(2)) and X-axis is

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  17. Find the area of the region bounded by the ellipse (x^(2))/(9)+(y^(2))...

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  18. The area bounded by the curves y^(2)=4a(x+a) and y^(2)=4b(b-x), where ...

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  19. Find the area bounded by the curve y=2x-x^2 and the straight line y=-x

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  20. Find the area of the smaller region bounded by the ellipse (x^2)/9+(y...

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