use-a-cas-to-find-the-exact-area-of-the-surface-obtained-by-rotating-the-curve-about-the-y-axis-if-y

Question

Use a $ CAS $ to find the exact area of the surface obtained by rotating the curve about the y-axis. If your $ CAS $ has trouble evaluating the integral, express the surface area as an integral in the other variable.

$ y = x^3 $ , $ 0 \le y \le 1 $

Amrita Bhasin · Accepted Answer

this question asked us to find the exact area of the integral by rotating the curve about the Y axis. What we know we need to do is we know we&#x27;re looking at the formula to pie Axe DX. We know two pies are constant. Therefore we can pull out. We know we&#x27;re looking at the integral from 01 and then we have acts times Diaz. I got nine X to the fourth because we have three x squared squared. So three squares, nine X squared is x the fourth so long as you can see now plugging this directly end tow Whatever online software using, we end up with 5.9194

Problem

Use a $ CAS $ to find the exact area of the surfa…

Problem 25 Medium Difficulty

Use a $ CAS $ to find the exact area of the surface obtained by rotating the curve about the y-axis. If your $ CAS $ has trouble evaluating the integral, express the surface area as an integral in the other variable.

$ y = x^3 $ , $ 0 \le y \le 1 $

Answer

$$\frac{\pi}{6}[3 \sqrt{10}+\ln (3+\sqrt{10})]$$

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