What is the surface area of the solid created by revolving #f(t) = ( 3t-1, t^2-2t+2), t in [2,3]# around the x-axis?

1 Answer
Apr 23, 2018

#=489392.457# Cubic units#

Explanation:

Parametric Equations

#x=3t-1#

#thereforet=(x+1)/3##color(green)(rarr(1)#

#y=t^2-2t+2#

Substitute in #y#

#y=(x+1)^2/9-2xx(x+1)/3+2#

When

#tin[2,3]##rarr##x in[5,8]# #color(blue) (" from "##color(green)((1)#

Determining the Volume of a Solid of Revolution

#V=piint_5^8((x+1)^2/9-2xx(x+1)/3+2)^2#

For this Integration, You will use #color(blue)("The Binomial Theorem and The Power Rule" #

#=489392.457# Cubic units#

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