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Area of Rectangle under a Parabola and Sectors in an Arc

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Proving the area of a shaded rectangle under a parabola and then differentiating the expression.
Minimizing the perimeter of sectors in an arc.

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Solution Summary

The area of a rectangle under a parabola is calculated and the perimeter of a sector in an arc is minimized.

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because parabola eqn. is given as:
y = 3 - x^2
Rectangle length is 2x and is symmetric about y axis, it means, the intersection points of parabola and rectangle are:
(x, 3-x^2) and (-x, 3-x^2)
therefore the area of shaded part:
A = area of the rectangle = length * width
width = ...

Solution provided by:
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
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