Problem

Find the coordinates of the centroids of the give…

Problem 20 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 $y=\sqrt{x}, y=0,$ and $x=9$

Answer

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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

in the given question, we have been asked to find the area off. Why is equal toe one by road off one minus nine x squared. So we know that areas in tickle off Why dx off appropriate Indo It's say here, Toby. So in this case, since we know that X belongs to the interval zero toe one by fix the integral will become integral from zero toe one by fix DX by squares wrote off one miner's nine x squared Now let you be three x From this we know that DX would be do you by three From here we know the limits off you ass zero to one. By do so, we can write that area would be equal toe one by three multiplied by tickle off Do you by square root off one minus You're squared where the limits are from zero to one by two. So this would be equal to one by three multiplied By signing worth off you buy one but the limits go from 0 to 1. By do so, area would be equal to one by three multiplied by signing words off one by go surely call toe one by three multiplied by bye bye six. So the answer would be the area would be by by 18 square unit.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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