Find the volume of the solid generated by revolving the regions bounded by the lines and curve about the x-axis

** y=x^2 ; y=0 ; x=3**

Find the volume of the solid generated by revolving the regions bounded by the lines and curve about the x-axis

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yar plz send me ur email i have typed the answer in

mathtype but if i paste hare, this window can not sport the format.

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Muhammad Tahir

I do believe that the bounded lines are y=x^2, x=0 ( and not y = 0 which is x axis) and x=3.

The axis of revolution is x or y = 0.

Let us consider a diffrential circular disk at a distance x from the origin, whose thickness is dx and whose radius is y = x^2. Then the differential volume of the differential circular disk is dV = pi*y^2*dx or pi*(x^2)^2 dx =pi*x^4*dx

So to get the volume of the solid of the curve y = x^2 between x=0 and x=3 , we have to integrate pi*y^2*dx between x=0 and x=3 . Or

V = integrate dV, between x=0 and x=3.

=Integrate pi*y^2dx between x=0 to x=3

= Integrate pi*x^4 dx between x=0 and x= 3.

= {[(pi*x^5/5)+C] at x=3} - {[(pi*x^5/5)+C] at x=0}, where C is the constant of integration.

=pi*3^5/5 -pi*0^5/5

= 48.6pi - 0

=**152.681403 cubic units**, taking the value of pi = 3.141592654 a constant of the circle.

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