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MAT 132 Midterm: MAT 132 SBU Exam Midterm 2sol

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turquoisegnu128
31 Jan 2019
School
Stony Brook University
Department
Mathematics
Course
MAT 132
Professor
All

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MAT 132 Full Course Notes
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MAT 132 Full Course Notes
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Document Summary

Compute the average value of the function sin x on the interval [0, ]. Let s be the region bounded by the graph of y = x2 + 1, the x-axis, and the lines x = 0 and x = 1. Find the volume of the solid obtained by rotating s about the x-axis. State at the beginning which method you are using. Solution: the sketch below shows the region s together with a typical cross section of the solid. The disk method is clearly the natural choice in this case. y = x2 + 1. The cross section at distance x from the origin has radius x2 + 1, and so its area is given by a(x) = (x2 + 1)2. Note: it is also possible (although very cumbersome) to use the shell method. It follows that the volume of the solid is and a lengthy calculation shows that this integral has value 28 /15.

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Related Questions

set up volume integrals using both cross-section method and cylindrical shell method.

1). The region bounded by y=sinx,x=pi/2 and y=0, rotated around the line x=-2.

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I need help solving some problems including area bounded by aregion and volume by cylindrical shells.

1) y = 3/x

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y=1/12x

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Find thevolume V of the solid obtained by rotating the regionbounded by the given curves about the specifiedline.

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3)Find thevolume V of the solid obtained by rotating the regionbounded by the given curves about the specified line.
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Find the volume V of the solid obtained by rotating theregion bounded by the given curves about the specified line.


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Find the volume V of the solid obtained by rotating theregion bounded by the given curves about the specifiedline.

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y=asin(bx^2)
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Use shells to find the volume V of S.

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Use the method of cylindrical shells to find thevolume of the solid obtained by rotating the region bounded by thegiven curves about the x-axis.
xy = 3
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Use the method of cylindrical shells to find the volume V ofthe solid obtained by rotating the region bounded by the givencurves about the x-axis.
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