Problem

The region bounded by the given curves is rotated…

02:03

Question

Answered step-by-step

Problem 41 Hard Difficulty

The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method.

$ x^2 + (y - 1)^2 = 1 $ ; about the y-axis

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Amrita Bhasin

Numerade Educator

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

Top Calculus 2 / BC Educators

Watch More Solved Questions in Chapter 6

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Video Transcript

okay, we know it's specified in the problem. The radius is X and the height is two time squirt of one minus X scored. Which means we're gonna be putting into the general formula, which is two pi times the integral from 01 off the height times the radius D of acts 01 are two bounds. Therefore, we end up with V is gonna be four pi times integral from 01 ax time scored of one less ex squirt. Where did the two go? You ask? Well, we remember the height was two time squared of our mess. X squared. I simply pulled the two out on the outside. It's a constant multiplied it by the original two pi toe end up with four pi on the outside Just a simple five days. Now we know in this context we can actually use U substitution, which you learned in a previous chapter. If you is one minus X squared than taking d'you, we end up with d'you. The derivative is negative to axe de axe. So what this means is that negative 1/2 to you is ex dx other words gonna be dividing four by two which means we end up with and remember, it's actually dividing for by negative, too, because it was negative. Two ex Texas do you So negative two pi times the integral from 10 There flips now because of the nature of the fact that we've taken u substitution. We've got negative value. Do the power rule In order to integrate increased exports by one divide by the new exponents, we end up with four pi divided by three

Get More Help with this Textbook

James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

Problem