Problem

Find the coordinates of the centroids of the give…

Problem 19 Easy Difficulty

Find the coordinates of the centroids of the given figures. Each region is covered by a thin, flat plate. The region bounded by $y=4-2 x, x=2,$ and $y=4$

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Calculus 2 / BC

Basic Technical Mathematics with Calculus

Chapter 26

Applications of Integration

Section 4

Centroids

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Video Transcript

we want to find the area bounded by Y equals four and y equals x two, the 2/3 in the first quadrant. This area right in here, so are left bound is going to be zero. And a right bound is gonna be where these two curves intersect. It will be at four equals x two, the 2/3. So it's so for X. Well, we can raise both sides to the third power four Cube gives a 64. The threes cancel and we're left with X squared. So X equals eight. And that will be our rate bound. So are integral. Goes from 0 to 8 and we're doing for minus X to the 2/3. And if we integrate, we get four x minus 3/5 x to the 5/3 and we'll pull you in eight and get four times eight minus 3/5 eight to the 5/3 and then minus plugging in zero, we just get zero. So this leaves us with 32 minus 3/5. Eight to the 5/3 is the same as saying eight to the 1/3 raised to the fifth Power and the cube root of eight is too, and to to the fifth is 32. So what we really have is 3/5 times 32. So are areas 30 to minus 3/5 times 32 which is going to be 2/5. Time is 32 or 64 over five, and that is our bounded area.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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