MATH-0042 Final: w11finalsol

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turquoisegnu128

9 Jan 2019

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Solutions to math 42 final exam march 14, 2011: (10 points) let r be the region in the xy-plane below the curve y = 2 (a) suppose s1 is the solid generated by rotating r about the x-axis. Set up two di erent integrals, each in terms of a single variable, representing the volume of s1. Cite the method used in each case, but don"t evaluate either integral. 1 + x2 and above the line y = First we nd the intersection points of the curves: 1/2 = 1/(1+x2) 2 = 1+x2 x = 1. We"ll take slices perpendicular to the x-axis and integrate with respect to x from 1 to 1. Vslice = (r2 outer r2 inner) x where router = y = 1. Therefore an integral representing the volume of the solid is. The volume of such a slice is given by.

Related Questions

Set up an integral representing the volume of the solid obtainedby revolving R about each of the following lines. Do not evaluatethe integral, just set it up. Indicate which method you are using(washer, shell, or disc)

Let D region in the xy plane bounded by the curves y = 4 - x^2and y = 2 - x

(a) the x-axis

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