I need help finding the volume of the solid generated by revolving the region bo

Question

I need help finding the volume of the solid generated by revolving the region bounded by y= square root(X) and the lines y=2 and x=0, about: a)the x axis b)the y axis c)the line y=2 Please help me and show all your work so I can understand whats happening and how to do it. I promise to rate back! THANKS!!!

Explanation / Answer

a) Volume = p integral (x = 0 ---> 4) [2^2 - (sqrt x)^2] dx = p integral (x = 0 ---> 4) (4 - x) dx = p (4x - x^2/2) | (x = 0 ---> 4) = p (16 - 16/2) = 8p b) y = sqrt x can be written as x = y^2 Volume = p integral (y = 0 ---> 2) (y^2)^2 dy = p integral (y = 0 ---> 2) y^4 dy = p y^5/5 | (y = 0 ---> 2) = 32p/5 c) y = sqrt x can be written as y = 2 - (2 - sqrt x) Volume = p integral (x = 0 ---> 4) (2 - sqrt x)^2 dx = p integral (x = 0 ---> 4) (4 - 4sqrt x + x) dx = p [4x - (8/3)x^(3/2) + x^2/2] | (x = 0 ---> 4) = p [16 - (8/3)4^(3/2) + 4^2/2] = p (16 - 64/3 + 8) = 8p/3 ;

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