Area Between CurvesExpected Educational ResultsBloom’s TaxonomyArea Between CurvesInvestigation 03CC BY-NC-SA 4.0

**Author**: John J Weber III, PhD
**Corresponding Textbook Sections**:

**Section 6.1**– Area Between Curves

**Objective 10–1**: I can set up the integral to compute the area of the region bounded by two or more curves.**Objective 10–2**: I can evaluate the integral to compute the area of the region bounded by two or more curves using FTC-II.**Objective 10–3**: I can use technology to estimate the area of the region bounded by two or more curves using FTC-II.

A modern version of Bloom’s Taxonomy is included here to recognize various different levels of understanding and to encourage you to work towards higher-order understanding (those at the top of the pyramid). All Objectives, Investigations, Activities, etc. are color-coded with the level of understanding.

Use the embedded DESMOS graph below:

Explain why the area between

and$y={x}^{3}-x+2$ $y=3x+2$ **must** .$\text{Area}0$ Solve the equation for

:$x$ .${x}^{3}-x+2=3x+2$ - Explain why there
**must**be three (3) solutions to the above equation. - Compare the solutions to the above equation to the
-coordinates of the intersections of$x$ and$y={x}^{3}-x+2$ . What do you notice? Explain.$y=3x+2$

- Explain why there
Explain why

does${\int}_{-2}^{2}({x}^{3}-x+2-(3x+2)){\textstyle \phantom{\rule{0.167em}{0ex}}}dx$ **not**represent the area between and$y={x}^{3}-x+2$ .$y=3x+2$ Compare

with${\int}_{-2}^{0}({x}^{3}-x+2-(3x+2)){\textstyle \phantom{\rule{0.167em}{0ex}}}dx+{\int}_{0}^{2}(3x+2-({x}^{3}-x+2)){\textstyle \phantom{\rule{0.167em}{0ex}}}dx$ .${\int}_{-2}^{2}|{x}^{3}-x+2-(3x+2)|{\textstyle \phantom{\rule{0.167em}{0ex}}}dx$ What do you notice? Explain.

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**Last Modified**: Thursday, 17 September 2020 2:48 EDT