2. Let D be the region between the parabolas y = x² +1 and y = 3–x² where |x|

2.<br>Let D be the region between the parabolas y = x² +1 and y = 3–x²<br>where |x| < 1. Drawing a sketch is recommended.<br>(a) Find a horizontal line y = C such that D is symmetric with respect to this line.<br>You need to evaluate C explicitly, but you do not need to prove that your answer is the<br>asserted value.<br>(b) Use Pappus' Centroid Theorem to find the volume for the solid of revolution<br>obtained by rotating D around the x-axis.<br>

Extracted text: 2. Let D be the region between the parabolas y = x² +1 and y = 3–x² where |x| < 1.="" drawing="" a="" sketch="" is="" recommended.="" (a)="" find="" a="" horizontal="" line="" y="C" such="" that="" d="" is="" symmetric="" with="" respect="" to="" this="" line.="" you="" need="" to="" evaluate="" c="" explicitly,="" but="" you="" do="" not="" need="" to="" prove="" that="" your="" answer="" is="" the="" asserted="" value.="" (b)="" use="" pappus'="" centroid="" theorem="" to="" find="" the="" volume="" for="" the="" solid="" of="" revolution="" obtained="" by="" rotating="" d="" around="" the="">

Jun 04, 2022

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2. Let D be the region between the parabolas y = x² +1 and y = 3–x² where |x|

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