Hello, everystepcalculus.com. We’re gonna do a problem in Yahoo regarding Shell Method and show you how that’s done in my programs. Index 8 to get to my menu. Then I scroll… if you go up, you get to the bottom of the alphabet because S is closer to W than A. And then we’re gonna find shell method, which is there. This problem is vertical axes number 2. Shows you this formula. They ask you if p(x) is the radius and is this second value given for X, and yes it is. We’re gonna add that alpha. 4 times X squared and the next value for Y is given. Alpha 24 times x minus 8, times X squared. I always show you what you did, and that was not correct so I have to go back and change it. Alpha 4 times x squared… I don’t know why it wasn’t right. Alpha 24 times X minus 8 times X squared. That’s better. Say it’s okay. Are the limits given, no, they’re not given. So we have to compute the limits, so we choose number 2. We do that by setting the… if no amount is given for the x axis of revolution then the vertical axis is 0; x=0. Anyways, we set the two functions equal to each other and then solve for x, when x equals 0 or 2. That’s where these functions intersect the X values where the Intersect. And so the height then needs to be recalculated. Height is the original function less than p(x) which equals this here. And then we’re ready to do our here’s the limit, 0 and 2, we do the calculation. Here’s the volume for the solid, the formula, notice x is for the radius and this is for the heights. And we multiply them together, we get this here. And we do the integration, which is this this: 8x cubed minus 3x to the fourth. And then at x=2, I’ll show you, these quotation marks here are you’d put parenthesis in there because you’re substituting 2 for all the x values. That equals 32 pi. And x=0, you substitute that in there, becomes 0 of course, so the answer is 32 pi. Have a good one.