3 years ago

Problem of the Day 7.7

Mathematics

1 answer:

Grace [21]3 years ago

3 0

Answer:

576

Step-by-step explanation:

18 x 32 = 576

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Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the

insens350 [35]

Answer:

So, the volume V is

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Step-by-step explanation:

We have that:

$y=7x\\\\y=0\\\\x=1\\\\x=-4\\$

We have the formula:

$V=2\pi\int_a^b x(g(x)-f(x))\, dx\\\\g(x)>f(x).$

We calculate the volume V, we get

$V=2\pi\int_a^b x(g(x)-f(x))\, dx\\\\V=2\pi\int_0^1 x(7x-0)\, dx\\\\V=2\pi\int_0^1 7x^2\, dx\\\\V=2\pi\cdot 7\left[\frac{x^3}{3}\right]_0^1\\\\V=14\pi\left(\frac{1}{3}-\frac{0}{3}\right)\\\\V=\frac{14\pi}{3}$

So, the volume V is

$V=\frac{14\pi}{3}$

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