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Problem 4 Medium Difficulty

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

$ y = x^3 $ , $ y = 0 $ , $ x = 1 $ , $ x = 2 $

Answer

$V=\frac{62 \pi}{5}$

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Video Transcript

we know that the general formula for volume is gonna be our bounds from A to B which you just cases wanted to to pi times our radius acts times our height acts cute times, DX This is the general formula. We just plugged directly at pull out our constant, which we know is to pie Simplify x times x cubed just simply x the fourth. Now we know we're gonna be using the power rule to integrate, which means we increase the experiment by one. So to the fifth divide by the new exponents, which means now we can plug in so plug in our bounds. Constant still on the outside. Work. Stay. Now we have two pi times 31 divided by five which gives us V is 62 pi divided by five