Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

Let $ S $ be the solid obtained by rotating the region shown in the figure about the y-axis. Sketch a typical cylindrical shell and find its circumference and height. Use shells to find the volume of $ S $. Do you think this method is preferable to slicing? Explain.

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Amrita Bhasin

Numerade Educator

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

02:52

Wen Zheng

Calculus 2 / BC

Chapter 6

Applications of Integration

Section 3

Volumes by Cylindrical Shells

Missouri State University

Harvey Mudd College

Boston College

Lectures

03:20

Let $S$ be the solid obtai…

01:56

Let $ S $ be the solid obt…

Let V be the volume of the…

03:57

01:51

Let $ V $ be the volume of…

08:33

Let $V$ be the volume of t…

04:26

02:46

Find the volume of each so…

given a figure that looks something like Thus we know that if we sketch the cylindrical shell, it probably looks something like this. Why is sign of X squared as given in the problem? Therefore, what we know, given this is that if the circumference is to pie attacks, the height is sign of ax squared. Those are two of the things as part of the answer thin. The volume is from our bounds zero to square root of pi to pi X times sign of ax squared As I just said earlier, we're just multiplying these two, which I announced. Now we know that when we integrate we we can first pull out our Constance so pi times the integral from zero to pie of sine of t DT Remember, the integral of sine is pretty straightforward. It's simply negative co sign of tea and then we all said the pile on the outside from zero to pie, which gives us now we can plug in pied times negative coastline of pi plus Ron which is simply pipas pie which is to pie

View More Answers From This Book

Find Another Textbook