Problem

For the following exercises, compute the center o…

Problem 260 Easy Difficulty

For the following exercises, compute the center of mass $\overline{x} .$
$\rho=1$ for $x \in(-1,3)$

Answer

$\overline{x}=1$

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus

Chapter 2

Applications of Integration

Section 6

Moments and Centers of Mass

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Video Transcript

So we went to calculate the center of mass off a search in La Mina knowing that its density is equal to one and we want to do so in the interval. Negative. 123 Sorry. Off ex native from negative. 123 So we want to find X with a lineup of it. And we know that this particular coordinate this interview, my ass, it's gonna be equal to the moment with respect to the Y axis divided by the total mass of de la manana. So let's find out this trick wanted his first. So the total must've de la Mina is defined as robe Sorry as integral from a TV of Rome Thames FX. The ex says we're not given any information about F effects. We must assume that it's it is equal to one. Genesis will have the integral from native 123 off one Sorry of Roe the ex we know row with the consent over here. So we'll have just row times the integral from native 123 the ex This just gonna be grow temps exit violated from native 123 And in this case is gonna be for a row. Now let's find a moment with respect to y axis. In this case, the moment would respect to the Y axis. It's gonna be the integral sorry road. Tim's an integral from a TV off Ex Temps ffx DX, which in this case can be re written as the ISRO Terms of integral from native 123 affects the X. We know that the inter roll effects it's just gonna be excess quarter. You're right. I'd like to violated from native 123 which is road divided by two times nine minus one, which is just equal to for a row. And if we plunk all of these two ballots over here, we found out that for row, but by four row sickle to one. Therefore the center of mess, he said X equal to one

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