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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 $

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Calculus 2 / BC

Chapter 8

Further Applications of Integration

Section 2

Area of a Surface of Revolution

Applications of Integration

Campbell University

Oregon State University

Boston College

Lectures

01:28

Use a CAS to find the exac…

0:00

Use a computer to find the…

01:00

Use a $ CAS $ to find the …

02:06

01:27

Use either a $ CAS $ or a …

01:12

Use either a CAS or a tabl…

03:35

01:29

Set up an integral for the…

02:11

Find the exact area of the…

01:18

05:35

01:17

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

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