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Problem 20 Medium Difficulty

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

$ x = 2y^2 $ , $ x = y^2 + 1 $ ; about $ y = -2 $

Answer

$V=\frac{16 \pi}{3}$

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Video Transcript

we know using the method of Shlain Driscoll shells. This means we have a radius and a height. Our radius is two plus. Why are height is gonna be one minus y squared? Which means if we're plugging into the formula to pi, times are bounds from negative one toe. One were multiplying radius times, height. So what this means is we have two plus y comes one minus y squared. It's pretty straight forward in terms of plugging in now, I would highly recommend simple Find this before taking the integral negative. Why cubed? Minus two. Why squared? Plus why Plus to do why now we integrate. We're gonna be using the power rule, which means increased the exponent by one divide by the new exponents, which means we have fee is 16 pie divided by three.