document.write( "Question 1189664: If R is a region between the graphs of the function f(x)=sinx and g(x)=cosx over the interval [0,pie]
\n" ); document.write( "a) find the area of rigion R
\n" ); document.write( "b)Define R as the region bounded above by the graph of the function f(x)=root x and below by the graph of the function g(x)=1 over the interval[1,4].find the volume of the solid of the revolution generated by revolving R around the Y-axis. \n" ); document.write( "

Algebra.Com's Answer #821280 by ikleyn(52794) $\"\"$ $\"About$

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\n" ); document.write( "If R is a region between the graphs of the function f(x)=sinx and g(x)=cosx over the interval [0,pie]
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\n" ); document.write( "\n" ); document.write( " In this post, I will solve problem (a), ONLY.\r
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document.write( "If you plot the graphs of the functions f(x) = sin(x) and g(x) = cos(x) over the interval [0,pi],\r\n" );
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document.write( "you will see that  g(x) >= f(x)  at 0 <= x <=   and  g(x) <= f(x)  at  <= x <= .\r\n" );
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document.write( "Also, you can get it algebraically.\r\n" );
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document.write( "In any case, the area of the region R is the sum of two integrals\r\n" );
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document.write( "    area(R) =  + .\r\n" );
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document.write( "First integral equals\r\n" );
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document.write( "    (sin(x) + cos(x))  from 0 to ,  which is   - 1 = .\r\n" );
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document.write( "Second integral equals\r\n" );
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document.write( "    (-cos(x) - sin(x))  from  to ,  which is  1 +  = .\r\n" );
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document.write( "After adding the integral values, we get\r\n" );
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document.write( "    area(R) =  +  =  = 2.828427  (rounded).    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Part (a) is solved.\r
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