MAT136H1 Chapter 2c: Class 2C - Notes

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ultramarineelephant806

25 Jul 2018

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Class (cid:884)(cid:1855) ~ volumes of solids of revolution. Region bounded between (cid:1877)=(cid:882), (cid:1877)=sin(cid:4666)(cid:1876)(cid:4667), (cid:1876)=(cid:882), (cid:1876): (cid:4666)sin(cid:2870)(cid:4666)(cid:1876)(cid:4667)(cid:4667) (cid:1876, (cid:1876)(cid:4666)sin(cid:2870)(cid:4666)(cid:1876)(cid:4667)(cid:4667), (cid:1876) Consider the region lying between the curves (cid:1877)=(cid:886)(cid:1876) and (cid:1877)=(cid:1876)(cid:2870). For each line below, write an expressio(cid:374) that approxi(cid:373)ates the (cid:448)olu(cid:373)e of a slice (cid:449)ith (cid:858)thick(cid:374)ess(cid:859) (cid:1876). Consider the region bounded by (cid:2870) and (cid:4666)(cid:1876) (cid:883)(cid:4667)(cid:2870). Find the volume of the solid generated by rotating this region around the line (cid:1876)= (cid:883). Adding up the slices, we get an approximation for the. When we take the limit of the riemann sums, we get an exact value for the volume. (cid:4666)(cid:1876)+(cid:883)(cid:4667)(cid:4666)(cid:2870) (cid:4666)(cid:1876) (cid:883)(cid:4667)(cid:2870)(cid:4667) (cid:1876) (cid:1876)= (cid:883) Note : we chose to slice into pieces of width (cid:1876) instead of (cid:1877) to avoid rearranging equations. The shape of each slice can then be approximated as a cylindrical shell of thickness (cid:1876). total volume : (cid:884)

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Solve all please.