#35

Ok. So #35 is actually not an AB topic. However, the mistake we made in class was the bounds are 0 to 2 on the x and we did 0 to 3 when we found the interesection. If you alter this to match the x-values then you will get 7.6 something which is close to 8. However, shells are much easier than washers and can only be done in a washer problem about the y-axis (for now). So you could do this entirely in your calculator MUCH faster. The formula for shells is

2pi(integral (x(top-bottom))) and you would use the bounds of the intersection regardless of the limitations given in the problem. So this would be 0 to 3. You use the x values not the ys when revolving about y and doing shells.

Nothing needs to be squared or any of that. This is Alot simpler. It is a shortcut that you learn next year but could help save time this year. So in your calculator you would type.

fnInt(x(9-x^2 - (9-3x)),x,0,3) then multiply that by 2pi.

You don't have to learn this method. It will not actually be on the AP but if it makes more sense for this method than you can try it to check your work.