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Find the volume generated by revolving the regions bounded by the given curves about the $x$ -axis. Use the indicated method in each case.$$y=\sqrt{x}, x=0, y=2 \quad \text { (shells) }$$

Calculus 2 / BC

Chapter 26

Applications of Integration

Section 3

Volumes by Integration

Missouri State University

Harvey Mudd College

University of Nottingham

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

02:57

Use the shell method to fi…

03:11

02:56

03:46

02:21

Find the volumes of the so…

02:09

02:04

it makes perfect sense when you look at why? Because the square root of X. And that they want you to take the region between X Equal zero. Um and y equals two. So we're talking about this region in here, it makes perfect sense to use the shell method as we're revolving it around the X axis. Um so what's the show method? It's two pi the radius times the height. Uh In terms of why, why is it why? Because the radius of each one of these cylinders will be why? Units? Um Now when X equals zero, the square to zero gives you zero for y. And they also give you the other bound of Y equals two. Um Now the other piece that sort of tricky as you want to solve for X, which is actually just why squared? Um As we do this problem. So I think you could do two steps at once. For instance why times Y squared is why cubed. And then when you do the integral and you add one to the exponent and divide by your new exponents. Um that we just did two steps at once. And what I also think it's very easy about this problem is two to the fourth power or two times two is four will cancel out with this for So you're just left with two more to the left, which is just four. Are you do two to the fourth power? 16 divided by four is four. And then also the bound of zero, this gives you zero. So four minus zero is four times the two pi gives you a pie, which is the correct answer.

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In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

Use the shell method to find the volumes of the solids generated by revolvin…

Find the volumes of the solids generated by revolving the regions bounded by…

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The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

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Mount Everest weighs an estimated 357 trillion pounds

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A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

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