How do I find the volume of the solid generated by revolving the region bounded by y=x^2, y=0, and x=2 about the x-axis? The y-axis?

1 Answer
May 19, 2018

1)Volume=piint_0^2x^4*dx=(32/5)pi (unite)^3

2)Volume=piint_0^4[(2^2)_2-(sqrty^2)_1]*dy=piint_0^4[4-y]*dy=8pi (unite)^3

Explanation:

the rose region is revolving about the x-axis and y-axis

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1)when the shaded region revolving a bout x-axis

Volume=piint_a^by^2*dx

Volume=piint_0^2y^2*dx=piint_0^2x^4*dx=pi[1/5*x^5]_0^2

=pi[(32/5)-0]=(32/5)pi (unite)^3

2)when the shaded region revolving about the y-axis

Volume=piint_d^c[(x^2)_2-(x^2)_1]*dy

Volume=piint_0^4[(2^2)_2-(sqrty^2)_1]*dy

=piint_0^4[4-y]*dy=pi[4y-1/2y^2]_0^4

=pi[16-8]=8pi (unite)^3