The region under the curves #y=xe^(x^3), 1<=x<=2# is rotated about the x axis. How do you find the volumes of the two solids of revolution?
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"Suppose that I don't have a formula for #g(x)# but I know that #g(1)
= 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
May 5, 2017
There is only on solid of revolution generated by this description.
Explanation:
The volume is
Use the substitution
# = [pi/6 e^(2x^3)]_1^2#
# = pi/6(e^16-e^2)#
Use a calculator if you want a decimal approximation.
