document.write( "Question 1203141: The area between y=x² and y+x²=8 is rotated 360° about the x-axis. Find the volume produced \n" ); document.write( "

Algebra.Com's Answer #838462 by ikleyn(52905) $\"\"$ $\"About$

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\n" ); document.write( " The area between y=x² and y+x²=8 is rotated 360° about the x-axis.
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document.write( "The outer boundary is y = 8-x^2.\r\n" );
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document.write( "The inner boundary is y = x^2.\r\n" );
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document.write( "These two curves intersect when  \r\n" );
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document.write( "    8-x^2 = x^2,  8 = x^2+x^2,  8 = 2x^2,  x^2 = 8/2 = 4,  x =  = +/- 2.\r\n" );
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document.write( "In the interval  -2 <= x <= 2, both curve are above the x-axis.\r\n" );
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document.write( "Each vertical section  x= const  of this volume  (of this solid body)  is a RING \r\n" );
document.write( "with the inner radius  r= x^2  and the outer radius R = 8-x^2.\r\n" );
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document.write( "The area of this ring is   =  = .\r\n" );
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document.write( "The antiderivative is  of this function    is  F(x) = .  \r\n" );
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document.write( "The integral from  -2  to  2  is the difference  \r\n" );
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document.write( "    F(2) - F(-2) = () - () =  =  =  = .\r\n" );
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document.write( "Thus the desired volume is   =  = 536.1651  (rounded).    ANSWER\r\n" );
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