Explore BrainMass

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.

Please see the attached file for the fully formatted problems.


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.