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# Integration and Sums of Rectangles

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1. Given f &#8242;(x) = ex + (4/3)x^(-2/3) , find f (x) if f(1) = e.

2. Given f (x) = x2 + x +1
(a) Approximate the area between the curve of f and the x-axis on the interval [0,2] using 4 rectangles
and right point sums.
(b) Find the EXACT area between the curve of f and the x-axis on the interval [0,2] by using area as the
limit of a sum and summation formulas.

keywords: integration, integrates, integrals, integrating, double, triple, multiple

##### Solution Summary

Integration and Sums of Rectangles are investigated. The exact area between the curve and the x-axis on an interval is found.

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