Mathematics, 08.09.2020 14:01 moneykingmarco079
Let A be the bounded region enclosed by the graphs of f(x)=x, g(x)=x3 . Find the volume of the solid obtained by rotating the region A about the line x+2=0.
Answers: 3
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![V=2\pi\int\limits^1_0 {(x+2)(x-x^3)} \, dx\\\\V=2\pi\int\limits^1_0(x^2-x^4+2x-2x^3)dx\\\\V=2\pi(\dfrac{x^3}{3}-\dfrac{x^5}{5}+2(\dfrac{x^2}{2})-2(\dfrac{x^4}{4}))_0^1\\\\V=2\pi[(\dfrac{1^3}{3}-\dfrac{1^5}{5}+2(\dfrac{1^2}{2})-2(\dfrac{1^4}{4}))-(\dfrac{0^3}{3}-\dfrac{0^5}{5}+2(\dfrac{0^2}{2})-2(\dfrac{0^4}{4}))]\\\\V=2\times \pi \times({\dfrac{1}{3}-\dfrac{1}{5}+1-\dfrac{1}{2})\\V=3.96\ units^2](/tpl/images/0745/6267/71d5e.png)
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Let A be the bounded region enclosed by the graphs of f(x)=x, g(x)=x3 . Find the volume of the solid...
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