document.write( "Question 995439: Use integration method to find the volume generated by two curves, \"y%5E2=4x\" and \"y%5E2=4%282-x%29\" ,turning 360 degrees, setting x-axis as the pivot. \n" ); document.write( "
Algebra.Com's Answer #614221 by Alan3354(69443)\"\" \"About 
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Use integration method to find the volume generated by two curves, \"y%5E2=4x\" and \"y%5E2=4%282-x%29\" ,turning 360 degrees, setting x-axis as the pivot.
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\n" ); document.write( "\"graph%28300%2C300%2C-1%2C4%2C-1%2C4%2C2sqrt%28x%29%2C2sqrt%282-x%29%29\"
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\n" ); document.write( "You can see in the graph that the 2 curves are symmetrical about x = 1, and about the x-axis.
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\n" ); document.write( "--> find the volume of the left half rotated about the x-axis.
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\n" ); document.write( "\"y+=+2sqrt%28x%29\" from 0 to 1:
\n" ); document.write( "Using disks centered on the x-axis:
\n" ); document.write( "Vol = pi*r^2*dx
\n" ); document.write( "\"Vol+=+pi%2A%282sqrt%28x%29%29%5E2dx\"
\n" ); document.write( "\"Vol+=+4pi%2Axdx\"
\n" ); document.write( "\"INT+=+2pi%2Ax%5E2\"
\n" ); document.write( "--> Vol = 2pi per half
\n" ); document.write( "Total volume = 4pi cubic units.\r
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