x² + y2 = r2 tr A = 2 4r 3n [C

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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The shaded area below is a semicircular area from your chart. Given that the equation for the
curve is ?2 +?2 =?2 prove using direct integration that the y coordinate of the centroid, ?̅, is
4r/3?  You must draw you differential element on the figure and label ?̃ , ?̃.

You must use integration to find the first moment. However, to save time, you may use the area
of the semicircle: ∫??=?=??2/2

x? + y? = r²
y
2
4r
Transcribed Image Text:x? + y? = r² y 2 4r
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