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Problem 36 Hard 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 = 1 + xe^{-x^3} $ , $ y = \arctan x^2 $

Answer

6.9234

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Video Transcript

this problem has specified that we should graph the functions to determine the intersection. Points we get over here. Negative. 0.57 comma, 0.31 floor and then up here. We got 1.391 comma, 1.94 Okay, now that we have the diagram in the intersection points, we know we can plug into the volume formula, which we know is pi times the lower bound to the upper bound on the outer radius. Word modesty in a radius squared. Okay, Out already squared, minus and already a squared. Using a calculator. We got 6.9234