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1. Consider the region bounded by the graph of y^2 = r^2 ?x^2 (a) When this region...

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Basic Math

1. Consider the region bounded by the graph of y^2 = r^2?x^2

(a) When this region is rotated about the x-axis a sphere ofradius r is generated. Use integration to find its volume V (b) Useintegration to find the surface area of such a sphere

2. Find the arc length of the curve y = 1 3 x 3/2 on [0, 60](

3. Consider the graph of y = x^3 . Compute the surface area ofrevolution about the x-axis over the interval [0, 2]

4. A spring whose equilibrium length of 15in. exerts a force of50 lbs when it is stretched to 20in. Find the work required tostretch the spring from 22in. to 24in.

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