Problem

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

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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

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

Topics

Applications of Integration

Calculus: Early Transcendentals

Chapter 8

Further Applications of Integration

Section 2

Area of a Surface of Revolution

Discussion

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Video Transcript

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're looking at the formula to pie Axe DX. We know two pies are constant. Therefore we can pull out. We know we'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

Amrita B.