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**1. The problem statement, all variables and given/known data**

The function is y = 2 - x. The region is bounded by x = 2 and x = 4. Calculate its volume by the shell method by rotating it by the x axis.

**3. The attempt at a solution**

This problem has been consuming my mind. I calculated it by the disc method and shell method but I got 2 different answers.

Disc method:

∫ pi (y^2) dx...Evaluated from 2 to 4

∫ pi(2 - x)^2 dx

Result : 8pi/3

Shell method:

∫ 2pi*y*x*dy......Evalluated from -2 to 0.

∫ 2pi(y^2) dy

Result : 16pi/3