document.write( "Question 438696: Summation: i=1 to 1000 (i^(1/3))\r
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Algebra.Com's Answer #303303 by richard1234(7193) $\"\"$ $\"About$

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Note that if we were to approximate the integral $\"int%28x%5E%281%2F3%29%2C+dx%2C+1%2C+1000%29\"$ , we can use 1000 rectangles of width 1, and sum from the right-hand endpoints. This approximation is actually equal to $\"sum%28i%5E%281%2F3%29%2C+i=1%2C1000%29\"$ , since the base of each rectangle is 1 and the height is x^(1/3).\r
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\n" ); document.write( "\n" ); document.write( "According to Wolfram Alpha,\r
\n" ); document.write( "\n" ); document.write( " $\"int%28x%5E%281%2F3%29%2C+dx%2C+1%2C+1000%29+=+7499.25\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"sum%28i%5E%281%2F3%29%2C+i=1%2C1000%29+=+7504.72\"$ (rounded to two decimal places) \n" ); document.write( "

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