Problem

Use a graph to find approximate $x$ -coordinates …

01:38

Question:

Problem 23 Easy Difficulty

Use a graph to find approximate $x$ -coordinates of the points of intersection of the given curves. Then use your calculator to find (approximately) the volume of the solid obtained
by rotating about the $x$ -axis the region bounded by these curves.
$$y=2+x^{2} \cos x, \quad y=x^{4}+x+1$$

Video Answer:

Answer

$$
\approx 23.7802
$$

Related Courses

Calculus 2 / BC

Essential Calculus Early Transcendentals

Chapter 7

APPLICATIONS OF INTEGRATION

Section 2

Volumes

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Watch More Solved Questions in Chapter 7

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

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Video Transcript

Okay, So for this problem, when you're asked to use the appropriate pieces to be able, Thio, find the volume. Given the fact that we have an outer radius of two plus X squared cosine X, we have an inner radius, which is going to be X to the fourth plus X plus one. And then if we look at the graph, we have X intercepts of approximately negative 1.28 78 I'm sorry, 79 and 0.8843 And so what we want to do is we want to set up our volume equation, so we're gonna be using the washer method for this. So if you recall, the washer is the volume equals pi from A to B of, um, are one squared minus are two squared d x. So we already have our our one in our are two. So are are one is simply just outer radius R two is inner radius and we're gonna be using the's um X, the X intercept. So 1.2879 So we're gonna have to plus X squared co sign X squared minus X to the fourth plus X plus one squared DX. And of course, we're using a at feature on the graphing calculator, so we find out that this is approximately 23.782

We have video lessons for 76.75% of the questions in this textbook

James Stewart

Essential Calculus Early Transcendentals

View More Answers From This Book

Find Another Textbook

Problem