Mathematics, 26.10.2020 17:10 caggh345
Calculate by double integration the area of the bounded region determined by the given pairs of curves. g
Answers: 2
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![= \int^4_{-2} [\frac{x+4}{4} - \frac{x^2}{8}] \ \ dx \\\\= \int^4_{-2} \frac{x+4}{4} \ dx - \int^4_{-2} \frac{x^2}{8} \ dx \\\\ = \frac{1}{4} \int^4_{-2} (x+4) \ dx- \frac{1}{8} \int^4_{-2} x^2 \ dx\\\\ = \frac{1}{4} (\frac {x^2}{2}+4x)^{4}_{-2}- \frac{1}{8} (\frac{x^3}{3})^{4}_{-2} \ dx\\\\ = \frac{1}{4} [(\frac {x^2}{2}+4x)^{4}_{-2}- \frac{1}{2} (\frac{x^3}{3})^{4}_{-2}] \ dx\\\\ = \frac{1}{4} [(\frac {x^2}{2}+4x- \frac{x^3}{6})^{4}_{-2}] \ dx\\\\= \frac{9}{2}\\](/tpl/images/0840/3865/4e77b.png)
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