Mathematics, 20.03.2020 03:56 Silkyruthie
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis. y = 7 x , y = 0, x = 1; about x = −4
Answers: 1
![V=2\pi\int_a^b x(g(x)-f(x))\, dx\\\\V=2\pi\int_0^1 x(7x-0)\, dx\\\\V=2\pi\int_0^1 7x^2\, dx\\\\V=2\pi\cdot 7\left[\frac{x^3}{3}\right]_0^1\\\\V=14\pi\left(\frac{1}{3}-\frac{0}{3}\right)\\\\V=\frac{14\pi}{3}](/tpl/images/0555/4007/374ef.png)
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