SOLUTION: Summation: i=1 to 1000 (i^(1/3)) Is this approximately equal to the integral: 1 to 1000 (x^(1/3))dx?

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Question 438696: Summation: i=1 to 1000 (i^(1/3))
Is this approximately equal to the integral: 1 to 1000 (x^(1/3))dx?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
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).

According to Wolfram Alpha,
int%28x%5E%281%2F3%29%2C+dx%2C+1%2C+1000%29+=+7499.25

sum%28i%5E%281%2F3%29%2C+i=1%2C1000%29+=+7504.72 (rounded to two decimal places)