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Numerade Educator

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Problem 13 Medium Difficulty

Find the exact area of the surface obtained by rotating the curve about the x-axis.

$ x = \frac{1}{3} (y^2 + 2)^{\frac{3}{2}} $ , $ 1 \le y \le 2 $

Answer

$=\frac{21 \pi}{2}$

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Video Transcript

before plugging into the integral. The first thing we should do is we should different. She ate 1/2 parentheses. Why squared plus two to the 1/2 in order to then be able to plug in to the integral. So we end up with differentiating This meant up with Y to the fourth plus two y Square, which means now we can plug it into our intro from 1 to 2 to pie. Why time squirt of one plus y to the fourth plus two y squared times D Wykes of the variables. Why not acts? Okay, now that we have this, we know that we can pull out the to pile on the outside. We have integral from 1 to 2. Why cute? That's why, again simplifying it. It's best to simply as much as possible for integrating, because now that we're integrating, we're taking the power rule. It's so much easier now that we don't have anything under a square root plug end. We end up with 21 pie divided by two