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If the region $ \Re = \{(x, y) \mid x \ge 1 , 0 \…

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Problem 26 Hard 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 = \ln (x + 1) $ , $ 0 \le x \le 1 $

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Calculus: Early Transcendentals

Chapter 8

Further Applications of Integration

Section 2

Area of a Surface of Revolution

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Video Transcript

this question asked us to find the exact area of the surface obtained by rotating the curve about the Y axis. What we know is that we're going to be looking at the fact that we have if X plus One is eating the Y than X is you the wife minus one, which means X prime or the derivative is each the Why? Because this is just a constant. So this interest derivative would just be zero. So now we have from our bounds of a to be lowered upper bound zero to natural log of two again, we get this because we pulled out the natural log by taking ecause we know eat times natural log simply cancels out and gives us one plugging this into your software. We end up with 3.69

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Problem

If the region $ \Re = \{(x, y) \mid x \ge 1 , 0 \…

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Related Courses

Calculus: Early Transcendentals

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Watch More Solved Questions in Chapter 8

Video Transcript

James Stewart

Calculus: Early Transcendentals

Heather Zimmers

Kayleah Tsai

Samuel Hannah

Joseph Lentino

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Heather Zimmers

Kayleah Tsai

Samuel Hannah

Joseph Lentino

James StewartCalculus: Early Transcendentals

Heather Zimmers

Kayleah Tsai

Samuel Hannah

Joseph Lentino

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