document.write( "Question 1163267: graph the following curves:
\n" ); document.write( "y=x, xy=1 and x=2
\n" ); document.write( "and determinethe area bounded using:
\n" ); document.write( "a)A vertical element
\n" ); document.write( "b)A horizontal element \n" ); document.write( "

Algebra.Com's Answer #787321 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "\r\n" );
document.write( "Sorry, I misread x=2 as y=2.  But here it is for y=2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We must break the area into two parts, so that in each part the\r\n" );
document.write( "ends of the elements are on the same two different curves throughout\r\n" );
document.write( "the area.  So the green line is the dividing line.  We will find the\r\n" );
document.write( "area of the region to the left of the green line and then find the\r\n" );
document.write( "area of the region to the right of the green line and add them together:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The area to the right of the green line is just an isosceles right triangle\r\n" );
document.write( "with each leg = 1 = base = height.  So the area is given by:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So the sum of the areas of the two parts are\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "-----------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Now we'll do it with horizontal elements.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Using horizontal element:\r\n" );
document.write( "\r\n" );
document.write( "We must solve the equations of xy=1 for x and y=x for x if we\r\n" );
document.write( "use horizontal elements. They are x=1/y and x=y.\r\n" );
document.write( "\r\n" );
document.write( "The region does not need to be broken up because one end of the\r\n" );
document.write( "horizontal element is on y=1/x throughout the area, and the other\r\n" );
document.write( "end of the horizontal element is on y=x throughout the area.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "

\n" );