document.write( "Question 1062026: Compute for the value of \r
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Algebra.Com's Answer #677069 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "1.  Let me show first how to calculate more simple integral \r\n" );
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document.write( "    .      (1)\r\n" );
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document.write( "    Change variables for polar coordinates x = ,  y = .\r\n" );
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document.write( "    Then dx*dy = , and the integral (1) becomes \r\n" );
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document.write( "     =  = (introduce new variable z = ) = .\r\n" );
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document.write( "    The internal integral is \r\n" );
document.write( "                                                          |\r\n" );
document.write( "     =   =  |         =  .\r\n" );
document.write( "                                                          |0\r\n" );
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document.write( "    Then the entire double integral (1) is   = .\r\n" );
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document.write( "2.  Now, let us start with the original integral  \r\n" );
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document.write( "    .      (2)\r\n" );
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document.write( "To calculate this integral, let me introduce the new coordinate system \r\n" );
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document.write( "   u = x,\r\n" );
document.write( "   v = .\r\n" );
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document.write( "Then\r\n" );
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document.write( "   x = u,  y = ;  dx = du, dy = , and the integral (2) becomes\r\n" );
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document.write( "   .\r\n" );
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document.write( "   The integral of \"u\" and \"v\" after the factor  was just calculated in the section #1.\r\n" );
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document.write( "   Hence, the final answer is  = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. The integral (2) is equal to $\"pi%2F6\"$ .\r
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