How do you find the volume of the solid generated when the regions bounded by the graphs of the given equations #y = 2/sqrtx, x=1, x=5# and the #x#-axis are rotated about the #x#-axis?

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Answer 1 · 2017-05-25T22:33:00

#V=4ln5pi#

The volume of revolution, #V#, given by a curve #y=f(x)# rotated about the #x#-axis between #b# and #a# is given by:

#V=piint_a^by^2# #dx#

Here #y=2/sqrtx rArry^2=4/x#, #b=5# and #a=1#

#thereforeV=piint_1^5 4/x# #dx=pi[4ln|x|]_1^5-4ln5pi-0=4ln5pi#