MAT136H1 Chapter Notes - Chapter 2c-3a: Product Rule, Differentiation Rules, Good Luck!!
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25 Jul 2018
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= 0, = sin(), = 0: (sin2()) , (sin2()), . Consider the region lying between the curves = 4 and =2. For each line below, write an expression that approximates the volume of a slice with thickness" . Consider the region bounded by 2 and ( 1)2. Find the volume of the solid generated by rotating this region around the line = 1. Volume of a slice = 2(1 +)(2 ( 1)2) . Note : we chose to slice into pieces of width instead of to avoid rearranging equations. The shape of each slice can then be approximated as a cylindrical shell of thickness . total volume : 2. It is 2( + 1)(2 ( 1)2) Limits of integration where the 2 curves intersect which will be the range of allowed. = 0. 5 or = 2 using quadratic formula ( + 1)(2 ( 1)2) .
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