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Area of the region bounded by the curve `y=2^(x),y=2x-x^(2),x=0` and `x=2` is given by

A

`(3)/(log 2)-(4)/(3)`

B

`(3)/(log 2)+(4)/(3)`

C

`2 "log" 2-(4)/(3)`

D

`2 log^(2)-(4)/(3)`

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The correct Answer is:
D
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OBJECTIVE RD SHARMA ENGLISH-AREAS OF BOUNDED REGIONS-Exercise
  1. The area of the region bounded by the curve y = |x - 1| and y = 1 is:

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

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  3. Area of the region bounded by the curve y=2^(x),y=2x-x^(2),x=0 and x=2...

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  4. Area lying in the first quadrant and bounded by the circle x^(2)+y^(2)...

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  5. A O B is the positive quadrant of the ellipse (x^2)/(a^2)+(y^2)/(b^...

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  6. Using integration, find the area of the region bounded by the line x...

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  7. The area cut off from a parabola by any double ordinate is k time th...

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  8. Area between the curve y=4+3x-x^(2) and x-axis in square units , is

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  9. If A is the area between the curve y=sin x and x-axis in the interval...

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  10. If A is the area lying between the curve y=sin x and x-axis between x...

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  11. The area of the loop between the curve y=asinx and x-axis is (A) a (B)...

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  12. Area (in square units) of the region bounded by the curve y^(2)=4x,y...

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  13. If A1 is the area of the parabola y^2=4 ax lying between vertex and th...

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  14. The area of the figure bounded by y=sin x, y=cos x is the first quardr...

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  15. The area bounded by the curves y=xe^(x),y=xe^(-x) and the line x=1 is

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  16. The areas of the figure into which the curve y^(2)=6x divides the circ...

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  17. Find the area (in sq. unit) bounded by the curves : y = e^(x), y = e^(...

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  18. The area of the region bounded by the Y-"axis" y = "cos" x and y = "si...

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  19. The positive value of the parmeter 'a' for which the area of the figur...

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  20. The vlaue of m for which the area included between th curves y^(2)=4ax...

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