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# Some computer algebra systems have commands that will draw approximating rectangles and evaluate the sums of their areas, at least if $x_{i}^{*}$ is a left or right endpoint. (For instance, in Maple use leftbox, rightbox, leftsum, and rightsum.)(a) If $f(x) = 1/(x^2 + 1)$, $0 \le x \le 1$, find the left and right sums for $n$ = 10, 30, and 50.(b) Illustrate by graphing the rectangles in part (a).(c) Show that the exact area under $f$ lies between 0.780 and 0.791.

## a. Specifically, $R_{10} \approx 0.7600$ $R_{30} \approx 0.7770,$ and $R_{50} \approx 0.7804$b. GRAPHc. 0.780 and 0.791

Integrals

Integration

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Oregon State University

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University of Michigan - Ann Arbor

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University of Nottingham

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Idaho State University

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Florida State University

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Integrals

Integration

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

Lectures

Join Bootcamp