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Let C(1) and C(2) be the graphs of the f...

Let `C_(1) and C_(2)` be the graphs of the functions `y=x^(2) and y=2x,` respectively, where `0le x le 1." Let "C_(3)` be the graph of a function y=f(x), where `0lexle1, f(0)=0.` For a point P on `C_(1),` let the lines through P, parallel to the axes, meet `C_(2) and C_(3)` at Q and R, respectively (see figure). If for every position of `P(on C_(1)),` the areas of the shaded regions OPQ and ORP are equal, determine the function f(x).

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The correct Answer is:
`f_(x)=x^(3)-x^(2)`
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ARIHANT MATHS ENGLISH-AREA OF BOUNDED REGIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let C(1) and C(2) be the graphs of the functions y=x^(2) and y=2x, res...

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  2. Area of the region {(x,y) in R^(2):ygesqrt(|x+3|),5ylex+9le15} is eq...

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  3. about to only mathematics

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  4. about to only mathematics

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  5. The area enclosed by the curve y=sinx+cosxa n dy=|cosx-sinx| over the ...

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  6. Let S be the area of the region enclosed by y-e^(-x^(2)),y=0, x=0 and ...

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  7. Let f:[-1,2]->[0,oo) be a continuous function such that f(x)=f(1-x)for...

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  8. Let the straight line x= b divide the area enclosed by y=(1-x)^(2),y=0...

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  9. The area of the region bounded by the curve y=e^x and lines x=0a n dy=...

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  10. The area of the region bounded by the curves y=sqrt[[1+sinx]/cosx] and...

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  11. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

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  12. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

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  13. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

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

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  15. The area (in sq. units) of the region {(x,y):y^(2)ge2x and x^(2)+y^(2)...

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

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  17. The area (in sq. units) of the quadrilateral formed by the tangents ...

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

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  19. The area bounded by the curves y=sqrt(x),2y+3=x , and x-axis in the 1s...

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

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  21. The area of the region enclosed by the curves y=x, x=e,y=(1)/(x) and t...

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