Hello, everystepcalculus.com. A problem from a student regarding Shell Method and the vertical axis system. I’m gonna show you how my programs do that one. I’ll do the X axes in another video. Index 8 to get to my menu, scroll up because we got to the bottom on the menu, and get to the S section, which is Shell Method, easier, quicker. Here’s Shell Method, and get a choice of x axes or vertical axes, I’m gonna do the vertical axes now. Number 2, there’s a formula for it, and there’s always two functions given. If not, you have to enter the second, which is generally 0. You have to press alpha before you enter anything in these entry lines here. Alpha, 2, times X plus 3 is the function given. And the other one we’re going to put is alpha 0. I will show what you’ve entered, you can change it if you want. I see it’s okay. Are limits given? Yes, they are given. Lower limit is alpha 1, upper limit is alpha 2. I’ll also show you that in case you made a mistake. See, that’s okay, and you get the radius of x, and the height is 2x+3, p(x) and h(x) are the functions. So we substitute that into the formula, which is right here. You had it just like this on your paper. And we’re gonna multiply the two functions together, we get this right here with the limits of 2 over 1. And now we do the integration which equals this right here over those limits. And X=2, you substitute 2 for all the X’s in the function. I have to use quotations here because that’s where the calculator does it, but you’re going to use parentheses around these 2’s here, because you’re substituting 2 for every x. That equals this which equals 68 pi over 3. And X=1, you’re gonna substitute 1 for all the x’s in there, which equals 13 pi over 3. Upper minus lower is 55 pi over 3. That’s the answer! Have a good one!