Mathematics, 29.06.2020 06:01 AM28
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Y = (4/9) x^2, y = (13/9) − x2; about the x-axis
Answers: 2
![V=\pi \int_a^b [(g(x))^2-(f(x))^2]dx](/tpl/images/0696/8222/e2321.png)
   (1)
![V=\pi \int_{-1}^{1}[(\frac{13}{9}-x^2)^2-(\frac{4}{9}x^2)^2]dx\\\\V=\pi \int_{-1}^1[\frac{169}{81}-\frac{26}{9}x^2+x^4-\frac{16}{81}x^4]dx\\\\V=\pi \int_{-1}^1 [\frac{169}{81}-\frac{26}{9}x^2+\frac{65}{81}x^4]dx\\\\V=\pi [\frac{169}{81}x-\frac{26}{27}x^3+\frac{65}{405}x^5]_{-1}^1\\\\V\approx8.06\ cubed\ units](/tpl/images/0696/8222/9ed0e.png)
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