Have I discovered the Tardis's secret?

[tanon]

Volume of y = 1/5 (x-12)^3 + 2.95 when rotating around the x axis in the range x = 7 to 12 is 959.964 as per WolframAlpha BUT y = 1/5 (x-12)^3 + 2.8 is 975.868 where as it should be less because the curve has shifted closer to the x axis and therefore should have less volume. It is bigger on the inside than the outside.

No solution.

 

[tanon]

Volume of y = 1/5 (x-12)^3 + 2.95 when rotating around the x axis in the range x = 7 to 12 is 959.964 as per WolframAlpha BUT y = 1/5 (x-12)^3 + 2.8 is 975.868 where as it should be less because the curve has shifted closer to the x axis and therefore should have less volume. It is bigger on the inside than the outside.

May have resolved this.

 

[HallsofIvy]

Yep, that's the tardis' secret all right!!

 

[tanon]

Yep, that's the tardis' secret all right!!

Volume of revolution about the x axis:- integrate (pi*(1/5(x-12)^3+2.95)^2 from 7.15 to 12.38 = 763.41 units cubed AND Volume of revolution about the x axis:- integrate (pi*(1/5(x-12)^3+2.85)^2 from 7.15 to 12.38 = 771.262 BUT the 2.85 is a vertical shift of the curve down by 0.1 so the Volume of revolution should be less not more. Bigger on the inside than it is on the outside.