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Problem 36 Hard Difficulty

Use a computer algebra system to find the exact volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

$ y = x^3 \sin x $ , $ y = 0 $ , $ 0 \le x \le \pi $ ; about $ x = -1 $

Answer

2$\pi\left(48-6 \pi-12 \pi^{2}+\pi^{3}+\pi^{4}\right)$

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Video Transcript

we know the formula for this for volume is gonna be two pi times the intro from our bounds A to B zero pie Times Radius, which is axe minus negative one, which is X plus one times height, which is X cubed sign of ex, both of which were given in the original problem. Now what we know is that we can type this into our calculator cause it's saying computer generate systems. This means Wolfram Alpha calculator, Dez most math way. Any sort of computer generated system. You could plug this end too, and you will end up with exact value, which again means no decimal places. No estimation, no rounding. What it means is that we direct pie out is the symbol pi. That's what exact means again. 3.14 is not exact. Exact is only exact when we write out exactly like pie. So using Pew triggering system, we would end up with us