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y = k(x - a)2 2. By direct integration, determine the centroid of the area shown below. Express your answer in b. terms of a and b. Ans. I = a/4, y = (3b)/10 %3D

y = k(x - a)2 2. By direct integration, determine the centroid of the area shown below. Express your answer in b. terms of a and b. Ans. I = a/4, y = (3b)/10 %3D

Elements Of Electromagnetics
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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**Problem Statement:** 2. By direct integration, determine the centroid of the area shown below. Express your answer in terms of \(a\) and \(b\). **Graph Description:** The graph illustrates a shaded region under a parabolic curve described by the equation \(y = k(x - a)^2\). The region is positioned in the first quadrant of a Cartesian coordinate system with axes labeled \(x\) and \(y\). - The parabola opens to the right, intersecting the \(y\)-axis at a height \(b\) and the \(x\)-axis at a distance \(a\). - The curve is symmetrical around \(x = a\). **Solution:** The coordinates of the centroid (\(\bar{x}, \bar{y}\)) of the shaded area are calculated as follows: - \(\bar{x} = \frac{a}{4}\) - \(\bar{y} = \frac{3b}{10}\)
Transcribed Image Text:**Problem Statement:** 2. By direct integration, determine the centroid of the area shown below. Express your answer in terms of \(a\) and \(b\). **Graph Description:** The graph illustrates a shaded region under a parabolic curve described by the equation \(y = k(x - a)^2\). The region is positioned in the first quadrant of a Cartesian coordinate system with axes labeled \(x\) and \(y\). - The parabola opens to the right, intersecting the \(y\)-axis at a height \(b\) and the \(x\)-axis at a distance \(a\). - The curve is symmetrical around \(x = a\). **Solution:** The coordinates of the centroid (\(\bar{x}, \bar{y}\)) of the shaded area are calculated as follows: - \(\bar{x} = \frac{a}{4}\) - \(\bar{y} = \frac{3b}{10}\)
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