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For the following exercises, use the theorem of Pappus to determine the volume of the shape.Rotating $y=m x$ around the $x$ -axis between $x=0$ and $x=1$

$\frac{m^{2} \pi}{3}$

Calculus 2 / BC

Chapter 6

Applications of Integration

Section 6

Moments and Centers of Mass

Missouri State University

Harvey Mudd College

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Boston College

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

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For the following exercise…

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02:59

Find the volume of the sha…

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Okay, so we're asked to rotate. Why is equal to M X across the y axis or the X axis? I mean, So if why is he with MX? We rotate across the white or the x axis. So we have something like this. So it looks like a cone. Okay, So based on this, our area is this This looks like a triangle. So that's 1/2. See, this point here is one comma m based on tight. So we have 1/2 1 time, um, is equal to a So that's, um, over to our center of ass. If we have a triangle with purchases on these ends, it becomes see, So we have X one, which is oh, plus one plus one. All over. Three men. Zero still plus M J R. Y points over three. This just becomes to over three comma m over three. Okay, Now the distance traveled by the senator. Mess is a circle with radius em over three. Okay, so our distance this becomes to party. Time's over three, but you comes to hi. M time over. Great. Okay. And based on Durham of populace, we have a volume of a time feet which is equal to em over to attempt to, um to pie am over three becomes pie am squared over three.

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