Moments and Centroids LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1">Problem 4-27</Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Obtain the centroid (geometric center) of the planar region bounded by the graphs of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEkc2luRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJ0YyRjItSSNtb0dGJDYtUSIsRidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0Y+LyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRJGNvc0YnRi9GMkY1RjI=, 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.
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1">Visualization</Text-field> JSFH Type LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEkc2luRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJ0YyRjJGMg== Context Menu: Plots\342\211\273Plot Builder Control-drag LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEkY29zRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJ0YyRjJGMg== onto the graph. Hold Shift key, drag mouse to rubber-band that part of the graph in 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. JSFH NiQtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kieEdGKC1JJGNvc0dGJUYp ; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= ;
JSFH
<Text-field style="Heading 1" layout="Heading 1">Formulae</Text-field> JSFH If LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is the area of the plane region bounded by LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSIsRidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJnRidGL0YyRjVGPQ== with LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUS8mR3JlYXRlckVxdWFsO0YnRj0vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkUvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVC1GLDYlUSJnRidGL0YyRjVGPQ==, and 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 then the coordinates of the centroid are: 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
JSFH
<Text-field style="Heading 1" layout="Heading 1">Solution from First Principles</Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JKG1zdWJzdXBHRiQ2Jy1GNjYtUSsmSW50ZWdyYWw7RidGOS9GPFEmdW5zZXRGJy9GP0ZWL0ZBRjEvRkNGVi9GRUYxL0ZHRlYvRklGVi9GS1EmMC4wZW1GJy9GTkZobi1GIzYsLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZgby1JI21uR0YkNiRRIjNGJ0Y5LUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkhGZ25GaW4tRiw2JVEnJiM5NjA7RicvRjBGPUY5LUY2Ni1RIi9GJ0Y5RjtGPkZYRkJGREZGRkgvRktRLDAuMTY2NjY2N2VtRicvRk5GYXAtRmNvNiRRIjRGJ0Y5Ri8vJStmb3JlZ3JvdW5kR1EsWzIwMCwwLDIwMF1GJy8lLHBsYWNlaG9sZGVyR0YxRjItRiM2KUZpb0ZdcEZjcEYvRmZwRmlwRjIvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLyUvc3Vic2NyaXB0c2hpZnRHRl9xLUkobWZlbmNlZEdGJDYkLUYjNigtRiw2JVEkY29zRidGXHBGOS1GY3E2JC1GIzYkLUYsNiVRInhGJ0YvRjJGOUY5LUY2Ni1RKCZtaW51cztGJ0Y5RjtGPkZARkJGREZGRkhGX29GYW8tRiw2JVEkc2luRidGXHBGOUZqcUY5RjlGZm8tRjY2LlEwJkRpZmZlcmVudGlhbEQ7RidGL0YyRlVGVy9GQUZWRlkvRkVGVkZlbkZmbkZnbkZpbkZeckY5 Expression palette: definite integral template Context Menu: Assign Name LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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 Expression palette: definite integral template Context Menu: Assign Name LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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 Expression palette: definite integral template Context Menu: Assign Name LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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 Obtain 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 and 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 by implementing the appropriate divisions. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=