document.write( "Question 398002: The Question:
\n" ); document.write( "Find the area bounded by 1-e^(-2x) in the interval x = -1 to x = 1.\r
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Algebra.Com's Answer #282010 by richard1234(7193) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"graph%28200%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+1+-+e%5E%28-2x%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "The area is normally given by $\"int%28%281+-+e%5E%28-2x%29%29%2C+dx%2C+-1%2C+1%29\"$ . However, part of the area is counted as negative, so we must put a negative wherever $\"1+-+e%5E%28-2x%29+%3C+0\"$ .\r
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\n" ); document.write( "\n" ); document.write( "The function goes below the x-axis when $\"x+%3C+0\"$ , so I'll split into two integrals:\r
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(There'll be lots of negative signs involved so I just rewrote the first integral)\r
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\n" ); document.write( "\n" ); document.write( "To evaluate the indefinite integral $\"int%28%281-e%5E%28-2x%29%29%2C+dx%29\"$ , begin with the substitution $\"u+=+-2x\"$ , $\"du+=+-2dx\"$ . Replacing dx, we obtain\r
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\n" ); document.write( "\n" ); document.write( "I'll let you finish off the problem by evaluating at the bounds (the rest is just arithmetic and applying the fundamental theorem of calculus). \n" ); document.write( "

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