document.write( "Question 1145007: Solve by integration \"dx%2Fdt+=+t%28x+-+2%29\" \n" ); document.write( "
Algebra.Com's Answer #766186 by Edwin McCravy(20060)\"\" \"About 
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document.write( "\"dx%2Fdt+=+t%28x+-+2%29\"\r\n" );
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document.write( "Multiply both sides by dt:\r\n" );
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document.write( "\"dx+=+t%28x+-+2%29%2Adt\"\r\n" );
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document.write( "The term on the right side contains two variables, t and x. We must get rid\r\n" );
document.write( "of the other variable besides the variable of the differential.  The variable\r\n" );
document.write( "of the differential on the right side is t (because we have dt), so we must\r\n" );
document.write( "get rid of the (x - 2) factor.  So we divide both sides by (x - 2):\r\n" );
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document.write( "\"dx%2F%28x-2%29+=+%28t%28x+-+2%29%2Adt%29%2F%28x-2%29\"\r\n" );
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document.write( "\"dx%2F%28x-2%29+=+%28t%28cross%28x+-+2%29%29%2Adt%29%2F%28cross%28x-2%29%29\"\r\n" );
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document.write( "\"dx%2F%28x-2%29+=+t%2Adt%29\"\r\n" );
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document.write( "We integrate both sides:\r\n" );
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document.write( "\"int%28dx%2F%28x-2%29%29\"\"%22%22=%22%22\"\"int%28t%5E%22%22%2Adt%29%29\"\r\n" );
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document.write( "We use the formula \"int%28du%2Fu%29\"\"%22%22=%22%22\"\"%22ln%7Cu%7C%22%2BC\" on the left side,\r\n" );
document.write( "and we use the formula \"int%28u%5En%2Adu%29\"\"%22%22=%22%22\"\"u%5E%28n%2B1%29%2F%28n%2B1%29%2BC\" on the right side:\r\n" );
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document.write( "\"ln%28abs%28x-2%29%29=t%5E2%2F2%5E%22%22%2BC%5B1%5D\"\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2Ce%5E%28t%5E2%2BC%5B1%5D%29=abs%28x-2%29%29\"\r\n" );
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document.write( "Since the left side is positive, we can dispense with the absolute value on the\r\n" );
document.write( "right side and require that x>2.\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2Ce%5E%28t%5E2%2BC%5B1%5D%29=x-2%29\"\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2Ce%5Et%5E2%2Ae%5EC%5B1%5D=x-2%29\"\r\n" );
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document.write( "Since eC1 is an arbitrary constant, we can let it be C.\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2CCe%5Et%5E2=x-2%29\"\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2Cx=Ce%5Et%5E2%2B2%29\"\r\n" );
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document.write( "Edwin
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