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The given curve is rotated about the y-axis. Find the area of the resulting surface.

$ x^{\frac{2}{3}} + y^{\frac{2}{3}} = 1 $ , $ 0 \le y \le 1 $

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$$\frac{6}{5} \pi$$

Calculus 2 / BC

Chapter 8

Further Applications of Integration

Section 2

Area of a Surface of Revolution

Applications of Integration

Missouri State University

Harvey Mudd College

Idaho State University

Boston College

Lectures

01:41

The given curve is rotated…

06:27

05:41

14:05

01:18

Find the exact area of the…

05:35

02:11

01:09

02:50

01:27

01:17

this question asked us to use the bounds of 01 and find the area of the resulting surface. Given the fact that the curve is retained about the Y axis. What we know is we're looking from 0 to 1 is our two bounds and then we have two pi. We have the original expression and then we have this multiplied by the square root of one plus one minus y two. The 2/3 over Why the 2/3 do you? Why, We know he could write this out as to pie times the integral from 0 to 1. The reason why two pies on the outside is because estate in the textbook, because it is a constant, it doesn't need to be integrated. It could just be pulled out and then be multiplied by what's in the end. Okay, What we know we now have is U substitution if you is one minus one of the 2/3 member usually used u substitution with what's in parentheses. As you can see over here, do you is negative 2/3 wide to the negative 1/3 d Y. This now means that we have negative 6/5 spy times and then our upper minus or lower bound. This is equivalent to six over five pi the negative negative cancer.

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