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Let C(1 )and C(2) be two curves passing ...

Let `C_(1 )and C_(2)` be two curves passing through the origin as shown in the figure. A curve C is said to ‘‘bisect the area’’ the region between `C_(1) and C_(2)`, if for each point P of C, the two shaded regions A and B shown in the figure have equal areas. Determine the upper curve `C_(2)`, given that the bisecting curve C has the equation`y = x^(2)` and that the lower curve `C_(1)` has the equation `y = x^(2)//2.`

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The correct Answer is:
`(16/9)x^(2)`
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MOTION-AREA UNDER THE CURVE-EXERCISE -3
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  2. Consider the collection of all curve of the form y = a – bx^(2) that p...

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  3. For the curve f(x) = 1/(1+x^(2) , let two points on it are A(alpha, f(...

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  4. Let ‘c’ be the constant number such that c gt 1. If the least area ...

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  5. If y=f(x) is a monotonic function in (a,b), then the area bounded by t...

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  6. For what values of a in [0, 1] does the area of the fiqure bounded by ...

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  7. A figure is bounded by the curves y =|sqrt2 sin((pix)/4)|,y=0, x=2&x=4...

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  8. The line 3x +2y=13 divides the area enclosed by the curve, 9x^2+4y^2-1...

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  9. Find the area bounded by the curve y = xe^(-x^2) , the x-axis, and the...

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  10. A polynomial function f(x) satisfies the condition f(x+1)=f(x) + 2x + ...

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  11. Find the equation of the line passing through the origin and dividing ...

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  12. Consider the curve y=x^n where n > 1 in the 1^st quadrant. Ifthe areab...

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  13. In the adjacent figure the graph of two function y=f(x) and y=sin x ar...

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  14. If An be the area bounded by the curve y=(tanx^n) ands the lines x=0,\...

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  15. Find the whole area included between the curve x^2)y^(2) = a^(2)(y^(2)...

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  16. Let C(1 )and C(2) be two curves passing through the origin as shown in...

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  17. Consider the two curves y = 1//x^(2) and y = 1//[4(x-1)]. At what v...

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  18. If A = [[ln(a-1),0],[0,ln(b-1)]], then A^(-1) is :

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  19. If z is a complex number such that z = ln(a – 1) + iln (b – 1) then ar...

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  20. {:(,"Column - I", "Column - II"),("(A)" ,"The area bounded by curve","...

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