Let A be the bounded region enclosed by the graphs of f(x)=x, g(x)=x3 . Find the volume of the solid obtained by rotating the region A about the line x+2=0.

Given :

A be the bounded region enclosed by the graphs of and .

To Find :

The volume of the solid obtained by rotating the region A about the line x+2=0 .

Solution :

Point of intersection of f(x) and g(x) is 0 and 1 .

Volume of solid is given by :

Here , a and b is point of intersection and a = 1 and b = 0 .

Putting all given values in above equation , we get :

Therefore , the volume of the solid obtained is .

Hence , this is the required solution .

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gimmee one of those gold crowns!

~coco