# Area of Rectangle under a Parabola and Sectors in an Arc

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 Preview

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 Summary

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

$2.19