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Problem 35 Medium Difficulty

Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then use your calculator to find (approximately) the volume of the solid obtained by rotating about the x-axis the region bounded by these curves.

$ y = \ln (x^6 + 2) $ , $ y = \sqrt{3 - x^3} $

Answer

89.023

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Video Transcript

As this problem is justified, we have graft. And now we have found the intersection points. Okay, now that we have the intersection points, we can set up our integral to figure out what volume it so pi times integral from lower bound negative. 4.9 to the upper bound 1.9 Ah, natural log of X to the sex plus two squared minus squirt of three. And then it's X cubed squared. Now you're definitely gonna need a calculator for this. It'll get 89.23