Area Between CurvesExpected Educational ResultsBloom’s TaxonomyArea Between CurvesInvestigation 01CC 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:

- Identify the shaded region representing the area under
on$f(x)=\mathrm{sin}(\pi x)$ .$[0,0.5]$ - Identify
.${\int}_{0}^{0.5}\mathrm{sin}(\pi x){\textstyle \phantom{\rule{0.167em}{0ex}}}dx$ - Identify the shaded region representing the area under
on$g(x)=2x$ .$[0,0.5]$ - Identify
.${\int}_{0}^{0.5}2x{\textstyle \phantom{\rule{0.167em}{0ex}}}dx$ - Identify the shaded region representing the area \textbf{between}
and$f(x)=\mathrm{sin}(\pi x)$ on$g(x)=2x$ .$[0,0.5]$ - Compare
with${\int}_{0}^{0.5}\mathrm{sin}(\pi x){\textstyle \phantom{\rule{0.167em}{0ex}}}dx-{\int}_{0}^{0.5}2x{\textstyle \phantom{\rule{0.167em}{0ex}}}dx$ .${\int}_{0}^{0.5}(\mathrm{sin}(\pi x)-2x){\textstyle \phantom{\rule{0.167em}{0ex}}}dx$ - What do you notice? Explain.

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