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A table gives the values of a function obtained from an experiment. Use them to estimate using three equal subintervals with (a) right endpoints, (b) left endpoints, and (c) midpoints. If the function is known to be an increasing function, can you say whether your estimates are less than or greater than the exact value of the integral?

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Sixta Kovacek
Sixta KovacekLv2
14 May 2020

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With a programmable calculator (or a computer), it is possible to evaluate the expressions for the sum 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 forand 100. Then guess the value of the exact area.

The region under from 0 to 1.

With a programmable calculator (or a computer), it is possible to evaluate the expressions for the sum 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 forand 100. Then guess the value of the exact area.

The region under from 0 to.

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