document.write( "Question 614983: A solid body has a cross-section which is in the shape of the region between the curves $\"y=x%5E2\"$ and $\"y%5E2=8x\"$ .\r
\n" ); document.write( "\n" ); document.write( "Using calculus, accurately calculate the area under the two curves, between the intersect points.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I plotted my graph and know that it need integrating but not sure how you would do both accurately...add the areas...subtract them? im abit lost \n" ); document.write( "

Algebra.Com's Answer #386835 by Theo(13342) $\"\"$ $\"About$

You can put this solution on YOUR website!
if you graph these curves, you will see that the region is between them as shown below:
\n" ); document.write( " $\"graph%28600%2C600%2C-5%2C15%2C-5%2C15%2Cx%5E2%2Csqrt%288x%29%29\"$
\n" ); document.write( "the interval is the value of x from 0 to 2.
\n" ); document.write( "you would integrate both equations and you would then take the integral from x = 0 to x = 2 of both equations and subtract the value of the lower equation on the graph from the higher equation on the graph.
\n" ); document.write( "in that interval, the higher equation is y = sqrt(8x) while the lower equation is y = x^2
\n" ); document.write( "so it would be the integral of sqrt(8x) - the integral of x^2 in the interval from x = 0 to x = 2.
\n" ); document.write( "that's my take on it.
\n" ); document.write( "i'm very rusty in calculus and don't know much more than that, but that's my best guess for your problem.
\n" ); document.write( "essentially, the area for the higher curve is between the x-axis and that curve.
\n" ); document.write( "the area for the lower curve is between the x-axis and that curve.
\n" ); document.write( "when you subtract the area of the lower curve from the area of the upper curve, you are taking the area that is between them and nothing else.
\n" ); document.write( " \n" ); document.write( "

\n" );