Find the volume bounded by two curves

[Gamma]

I have this problem bothering me. I am asked to find the volume bounded by two curves, when they were rotated about the y axis. I did it as usual.

Functions are y1 = cosx +1

[tex] y_2 = 2(\frac{x - \pi}{\pi}) ^2[/itex]

The way I did the problem is to find the volume of revolution of y1 and y2 first and then subtracting one from the other.


Plot is shown in the attachment. I keep getting that the volume created by y2, V2>V1.

which is not possible according to the graph.


I have done and checked this problem hundred times now and can not figure where I am going wrong. Please help.....

 

[lippyka]

The formula for the volume of revolution is V = $\pi \int_{a}^{b} (y_2^2 - y_1^2) dx$So in this case, it would be:V = $\pi \int_{0}^{\pi} (2(\frac{x-\pi}{\pi})^2 - (cosx + 1)^2) dx$Solving this integral, you should get V2 < V1, which is the correct result.