Find the volume of the solid obtained by rotating the region bounded by the curves #y=x^3# and #x#-axis in the interval #(1,2)#?

1 Answer
Mar 21, 2017

Volume is #18 1/7pi#

Explanation:

To find the volume of the solid obtained by rotating the region bounded by the curves #y=x^3#, the #x#-axis and the lines #x=1# and #x=2# turn around the #x#-axis,

we need to find area of the curve under the curve #y=x^3#, between #x=1# and #x=2#.

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As the same is rotated around #x#-axis, we will get the volume of the desired solid.

Hence this volume is #int_1^2pi(x^3)^2dx#

= #int_1^2pix^6dx#

= #pi[x^7/7]_1^2#

= #pi{2^7/7-1^7/7}=(127 pi)/7=18 1/7pi#