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find the volume of the bounded area of y=x^2 and y=2-x^2 about x=2
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\n" ); document.write( "Find the area under y = 2-x^2 and above the x-axis:
\n" ); document.write( "INT = 2x - x^3/3
\n" ); document.write( "Evaluate from -1 to 1
\n" ); document.write( "@1 --> 2 - 1/3
\n" ); document.write( "@-1 --> -2 + 1/3
\n" ); document.write( "-------------- Subtract
\n" ); document.write( "Area = 4 -2/3 = 10/3
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\n" ); document.write( "From that, subtract the area under y = x^2 from -1 to +1 [-1 and +1 are the intersections of the 2 curves]
\n" ); document.write( "----------
\n" ); document.write( "INT = x^3/3
\n" ); document.write( "Area = 1/3 - (-1/3) = 2/3
\n" ); document.write( "========================
\n" ); document.write( "Area between curves = 8/3 sq units
\n" ); document.write( "The 2 curves are symmetrical, so the centroid of the area is (0,1)
\n" ); document.write( "Use the Theorem of Pappus to find the volume:
\n" ); document.write( "Vol = 2pi*distance to centroid*area
\n" ); document.write( "Vol = 2pi*2*8/3 cubic units
\n" ); document.write( "Vol = 32pi/3 cubic units
\n" ); document.write( "=~ 33.51 CU \n" ); document.write( "