How would you determine the volume of the solid generated by rotating the region bounded by

Question

f(x)  =x^2 – 4x+ 5, x= 1,x= 4 and the x-axis, about the x-axis. State and explain which method can be used, shell, or washer method or both.

Answer 1

Step 1:

The curve equations are  , , ,  and about -axis.

Here the curve and .

The region is rotated about -axis.

Using shell method, it is necessary to change the curve as a function of  in terms of   to express the height and evaluate the integral.

It would be a complicated process, hence use washer method to find th volume of the solid.

Method of washer :

The volume of the solid  is , where  is the cross sectional area of the solid .

Outer radius .

Inner radius .

Integral limits are  and .

.

Volume of the solid is  cubic units.

Solution:

Volume of the solid is  cubic units.