Question 995439
Use integration method to find the volume generated by two curves, {{{y^2=4x}}} and {{{y^2=4(2-x)}}} ,turning 360 degrees, setting x-axis as the pivot.
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{{{graph(300,300,-1,4,-1,4,2sqrt(x),2sqrt(2-x))}}}
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You can see in the graph that the 2 curves are symmetrical about x = 1, and about the x-axis.
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--> find the volume of the left half rotated about the x-axis.
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{{{y = 2sqrt(x)}}} from 0 to 1:
Using disks centered on the x-axis:
Vol = pi*r^2*dx
{{{Vol = pi*(2sqrt(x))^2dx}}}
{{{Vol = 4pi*xdx}}}
{{{INT = 2pi*x^2}}}
--> Vol = 2pi per half
Total volume = 4pi cubic units.