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Applications of Integrals : Area of a region Bounded by Three Curves and Volumes of Solids of Revolution

Let R be the shaded region in the first quadrant enclosed by the graphs of y=e^(-x^2), y= 1-cos x, y-axis as shown in the figure above.
(a) Find the area of the region R.
(b) Find the volume of the solid generated when the region R is revolved about the x-axis.
(c) The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a square. Find the volume of this solid.

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Area of a region Bounded by Three Curves and Volumes of Solids of Revolution are investigated. The solution is detailed and well presented.

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