Axis

- WE WANT TO FIND THE STANDARD EQUATION OF THE ELLIPSE WITH FOCI (4,0) AND (-4,0), AND THE LENGTH OF THE MINOR AXIS IS 6 UNITS. THE STANDARD EQUATION OF AN ELLIPSE WILL TAKE ON TWO FORMS BASED UPON...

What we're going to do in this video is take the function y is equal to the cube root of x and then rotate this around the x-axis. And if we do that, we get a solid of revolution that looks...

Where we left off in the last video, we'd actually set up our definite integral to figure out the volume of this figure. So now we just have to evaluate it. And really the hardest part is...

Here we have the graph, or part of the graph, of y is equal to x squared again. And I want to find the volume of another solid of revolution. But instead of rotating around the x-axis this time, I...

- WE'RE GOING TO DETERMINE IF THE GRAPHS OF THE GIVEN EQUATIONS WOULD BE SYMMETRICAL ABOUT THE X-AXIS, Y-AXIS OR THE ORIGIN. AND FOR A QUICK REVIEW, HERE ARE THE THREE TESTS THAT WE'LL...

Let's do some more volumes of solids of revolutions. So let's say that I have the graph y is equal to square root of x. So let's do it, so it looks something like this. So that...

- WELCOME TO AN INTRODUCTION TO SYMMETRY ABOUT THE X AXIS, Y AXIS AND THE ORIGIN USING POINTS. LET'S BEGIN BY CONSIDERING THESE FOUR POINTS ON THE COORDINATE PLANE. MORE SPECIFICALLY,...

Now let's do a really interesting problem. So I have y equals x, and y is equal to x squared minus 2x right over here. And we're going to rotate the region in between these two...

What we're going to do in this video is generalize what we did in the last video. And, essentially, end up with the formula for rotating something around the X-axis like this using, what we...

So all I have to do is jump out of this plane and attack them, right? That's right, put on your parachute now. Don't be silly, there's plenty of snow on the ground....