Problem

The area of the region that lies to the right of …

View

Problem 48 Hard Difficulty

Repeat Exercise 47 for the curve $ y = (x^2 + 1)^{-1} - x^4 $.

Name: repeat exercise 47 for the curve y x2 1 1 x4
Uploaded: 2021-04-26
Duration: 2 min 9 s
Channel: Numerade
Description: Repeat Exercise 47 for the curve $ y = (x^2 + 1)^{-1} - x^4 $.

Answer

Area below the given curve and above the $x$ -axis is $\approx 1.2326$

Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Heather Z.

Oregon State University

Michael J.

Idaho State University

Watch More Solved Questions in Chapter 5

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

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Video Transcript

Alright based off of the problem, I'm trusting that are allowed to use a graphing calculator plus the equation is kind of awkward. X squared plus one to the negative first power. And then we have minus X. To the fourth hole account. I don't know how you would do this in your head and maybe there's some fancy math going on. But once you do that you can zoom in and we actually only care about the X coordinates. This must be an even function because it looks symmetric with the Y. Axis. And we care about negative .8692 positive .869. So that's what I'm gonna do. I'm gonna pull up my tool under my functions and sometimes you have to click around before you find where your integral is. Mhm. And I believe I typed that I remember that. So negative .8692 positive .869. Yeah. And uh you unfortunately I might have to re type this equation otherwise you can copy and paste it down. Um And then you also might want to tell the calculator that X. Is your independent variable. I'm sure some other calculators might do that for you. Um and I rounded these answers these bounds, so my answer might be off a little bit, but if I were rounding my answer I would write down 1.233. Rounding to three decim, otherwise you can copy down the whole thing. Um And it should make sense that that answer is correct because if you look at trying to zoom around and it's not letting me and alright, there we go. Uh That that looks about right, the area looks like it should be a little bit bigger than one but smaller than two. Um things like that. So 1.233 is what I would write down.

Gregory H.

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem