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Missouri State University

Harvey Mudd College

University of Nottingham

00:33

Dungarsinh Puthvisinh

If $f(x)=x+\sqrt{2-x}$ and $g(u)=u+\sqrt{2-u},$ is it true that $f=g ?$

01:38

Felicia Sanders

0:00

Jsdfio Klsfjwjf

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of what we've covered in this. So we're going to review area death washer and shell methods. So first to review just area. So if you're us to find the area, just know the formula area is equal to the integral from A to B Oh, ffx minus G of X dx. Okay, so this is just a formula. It's usually left minus right, right minus left, top minus spot. So this is our formula for area. One thing I want to review quickly for everything. If we have DX, that means we're using bars that look like this, their vertical. And that also means we have a Y equals equation. If we're using d Y, that means we have horizontal bars and we have an X equal equation. This is true, no matter what method you're using. The other thing to keep in mind is that the x and y of the d, x or D y tell you where you should take your bounds from. So those tell what variables in the bulls to use in the integral. Okay, so now that we kind of have this foundation and we have the basic formula for area, we're going to get into the more meat of what we learned in this section. So more of what we learned in this section Waas dis washing shell So starting with disc, you use disc when you are perpendicular I'm gonna really that is purple perpendicular and you're touching your access. Okay, this is when we use the disk method. The formulas for the dis method is volume is equal to the integral from a to B of pie times are mhm squared d x or do y we use washer? This is the next method washer when we are perpendicular to the axis And this time we are not touching in the equation for washer is that volume is equal to the integral from a to B of pie, times are x squared minus little are X squared. Yeah, And then the third method we learned was the shell method And you, you show when you are parallel Carollo to the access in the volume equation for shell is the integral from A to B of two pi, and then we have height of the shell times the radius, and then you either have d x or D y. So here's a good some tips for going through these problems here, The things you want to look for. Do I have y equals? Or do I have an X equals equation? If it is hard to solve the equations for the other variable, this is your first big hint. If it's a y equals equation, you're going to be with DX. If it's an X equals equation, you should default to D y. However, these you can solve these and switch them around. So once you identify what kinds of equations you have, what bars you use, then you can go on thio. Are I parallel to my access, or am I perpendicular? And if you're parallel, you use shell. And if you're perpendicular, you can pick between disk or washer. And that's going to depend on whether you're touching the access or not. Sometimes the question will tell you which method. If the question tells you, then you need to make sure you're drawing your lines to match what the question says. So then you need to decide either this way or this way to match the methods. So if they tell you show you need to pick whichever one of these bars is parallel to the axis. This would be DX. This would be d by to, and you want to match the method that it tells you to use. Okay, so this is just some general guidelines of how to get you through these questions. Um, usually you can come up with your own method. This is how I think about it. I look at the equations I'm given. I'm looking at it, the questions telling me which one to use. And I'm making sure I would suggest memorizing the conditions of when you can use disc washer purchase, show these air the formulas and also keep in mind how to find the area.

Arc Length and Surface Area

Integration Techniques

Trig Integrals

Trig Substitution

Integrating Rational Functions

25:33

23:12