Calculus - Integration: Volume by Rotating an Area (3 of 10) Ex. 3: y=x^2,y=x About the x-axis

Visit ilectureonline.com for more math and science lectures!
In this video I will find the volume bounded by y=x^2,y=x about the x-axis

[@webed0blood865]

holy shit!!!!
I thought I would never understand this topic.... but I DID!!!!
thanks a lot man!!

[@lauraramirez1013]

Hey! I just wanted to say thank you so much for taking the time to make these videos. I have a physics final and calc 2 this week and you've saved my life with these videos. I now understand everything better. You make it easier to understand, I love your videos THANK YOU!!

[@MichelvanBiezen]

Thanks for sharing and good luck on your finals.

[@Gunefy]

Thank you very much, it is very kind of you.

[@MasayoMusic]

The post- rotation image was hard to imagine. I wouldn't have come up with a cone as the final image.

[@mohsenamini3297]

Great job Mr. Michel.....Thanks

[@ianhockey6283]

I hope you do not mind me saying, but the second zero in the evaluation should have a negative sign in front of it. Not that it changes the final result.

[@MichelvanBiezen]

Since + 0 = - 0 = 0 it doesn't matter. But for any other value of course, it needs to be a negative. All comments are always welcome.

[@aram5642]

Around 6:30: am I right that the whole subtraction should be enclosed by brackets? because the lower limit (although zero in this specific case) has to be multiplied by pi as well.

[@user-uh8wk5uy9n]

Find the surface area due to the rotation of the area between f(x)=x^3 and g(x)=x

[@MichelvanBiezen]

Here is an easy and interesting way to solve such a problem: CALCULUS 3 CH 7.1 PAPPUS-GULDINUS THEOREM ua-cam.com/video/hVYE7XBhJ8Y/v-deo.html

[@siegregoirehien1890]

thank you so much sir but what i observed from the volume of the element is your meant the thickness is just # since the area itself is just (y2-y1)dx

[@user-uh8wk5uy9n]

Find surface area by rotate y=erf(x) about x axis
x from -1 to 1

[@aaronbourne1725]

What, if they ask for the volume swept out? Is it the same thing?

[@angelfabian2202]

SOOOOOOO helpful sir!

[@MichelvanBiezen]

Glad it helped! 🙂

[@anastaciathalia]

Amazing explanation ,thanks teacher!

[@MichelvanBiezen]

Thank you! 😃

[@unknown-zn5hu]

thank you so much

[@mathopedia7678]

Why this volume not equal when i rotated about y-axis ?
i suppose that the rotation of the same curve about y-axis and x-axis are equal ?????

[@MichelvanBiezen]

No, it depends on the shape of the object.

[@rickywang6354]

At the radius of the circle, you write (x^2-x^4),I know it right, Could you tell me why (x-x^2)^2 is wrong.?

[@MichelvanBiezen]

If you multiply out (x - x^2)^2, you will get a different result. (Try it)

[@rickywang6354]

Thank you very much. I mean, x-x^2 also is the radius of the circle, right?

[@MichelvanBiezen]

x^2 - x = 0 is the equation you get when you solve the 2 equations simultaneously. The solution to that equation represent where the 2 functions cross.

[@nebilgokdemir4527]

thank you! it is a great video

[@MichelvanBiezen]

You are welcome!

[@ramgcc3444]

Thank you sir

[@xs2278]

Its so hard to tell if its a washer

[@Soufilhodomeupai]

Thank you, really helped a lot. I'm not even native but i could understand you very well, congratulations!