What is the volume of the solid produced by revolving #f(x)=x^2, x in [0,4] #around the x-axis?

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Answer 1 · 2017-02-12T01:05:46

Volume #= (1024pi)/5 \ "unit"^3#

graph{(y-x^2)=0 [-4.5, 4.5, -2, 18]}

The Volume of Revolution about #Ox# is given by:

# V= int_(x=a)^(x=b) \ pi y^2 \ dx #

So for for this problem:

# V= int_0^4 \ pi (x^2)^2 \ dx #
# \ \ \= pi \ int_0^4 \ x^4 \ dx #
# \ \ \= pi \ [(x^5)/5]_0^4#
# \ \ \= pi/5 \ [x^5]_0^4#
# \ \ \= (1024pi)/5 #