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# With a programmable calculator (or a computer), it is possible to evaluate the expressions for the sums of areas of approximating rectangles, even for large values of $n$, using looping. (On a TI use the Is> command or a For-EndFor loop, on a Casio use Isz, on an HP or in BASIC use a FOR-NEXT loop.) Compute the sum of the areas of approximating rectangles using equal subintervals and right endpoints for $n$ = 10, 30, 50, and 100. Then guess the value of the exact area.The region under $y = x^4$ from 0 to 1

## $\sum_{i=1}^{n} f\left(a+\left(i-\frac{1}{2}\right)\left(\frac{b-a}{n}\right)\right)$

Integrals

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Florida State University

Integrals

Integration

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