# Integration and Sums of Rectangles

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1. Given f ′(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

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##### 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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