![V = \int\limits^2_ {-2}\pi (f(x))^{2} \, dx \\\\ = \pi \int\limits^2_ {-2} (f(x))^{2} \, dx \\\\ = \pi \int\limits^2_ {-2} (x(6 - x^{2})^{\frac{1}{2} })^{2} \, dx \\\\ = \pi \int\limits^2_ {-2} x^{2}(6 - x^{2}) \, dx \\\\ = \pi \int\limits^2_{-2} 6x^{2} - x^{4} \, dx \\\\ = \pi [\frac{6x^{3} }{3} -\frac{x^{5}}{5} ]\limits^2_{-2} \\\\ = \pi [(2(2)^{3}-\frac{(2)^{5}}{5})-(2(-2)^{3} - \frac{(-2)^{-5}}{5}) ] \\\\ = \pi[(16 - \frac{32}{5}) - (-16-(-\frac{32}{5}))] \\\\ = \pi[\frac{48}{5} - (-\frac{48}{5})]](/tpl/images/2614/9691/d340c.png)
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Mathematics, 10.01.2022 14:00 Winechou
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