Question

Find the area under the graph of the function over the given interval???
y=e^x;[-5,9]

Answer 1

so, have you talked about riemann sums?

Answer 2

Riemann sums? Slow down a bit, this is just basic integration.
\[\int\limits_{-5}^{9}e^xdx\]

Answer 3

can you write it down step by step please?

Answer 4

you have to cover those before you are allowed to integrate

Answer 5

no, you will have to work on this with us, we need to know where you are in class first

Answer 6

\[ \int\limits_{-5}^{9}e^xdx = e^9 - e^5 \]

Answer 7

so basically b-a

Answer 8

lol

Answer 9

Why on Earth would you use a Riemann sum for this?

Answer 10

that is the fundamental theorem of calculus in action

Answer 11

isn't it -1/e^9

Answer 12

sorry -1/e^5****

Answer 13

I made a mistake in my last one, it should be e^-5

Answer 14

because prior to integration you have to learn riemann sums

Answer 15

\[ \int\limits_{-5}^{9}e^xdx = e^9 - e^{-5} \]

Answer 16

I don't think I would want to do riemann sums with the exponential function involved :p

Answer 17

and @kevst3r, a negative exponent doesn't yield a negative answer, but due to FTC you have a minus un front

Answer 18

in other words, \[e^9-1/e^5\]

Answer 19

I was asking to see if we were allowed to use plain old integration(to us)

Answer 20

unless we could use finite amount of rectangles

Answer 21

-5 is probably better notation, but yes

Answer 22

i might be okay with that if the finite number is low

Answer 23

Yes @kevst3r, both your way and my way of expressing it are correct but I prefer keeping it on one line.

Answer 24

You have to learn sums prior to learning integration and memorizing the integrals so I just needed a reference point

Answer 25

i have another question can i just ask it here?

Answer 26

Sure

Answer 27

or do i have to create another question

Answer 28

ok nice

Answer 29

i have two more questions for you guys then i'm good

Answer 30

okay,
\[y=(1/2)x^2, y=-x^2+6\]

Answer 31

the answer is 16, but i'm not sure how you do this problem

Answer 32

Well how would you integrate 0.5x^2?

Answer 33

Sorry, I know this isn't relevant but can someone take a look at my question ? I really need help

Answer 34

^dude get off my question go make ur own

Answer 35

I did but no one ever replys this is the only way i can actually get some help

Answer 36

jesus christ

Answer 37

tom any advice for this problem?

Answer 38

how do you integrate something of the form \[x^n\]?

Answer 39

just to make sure
or to make a guess
you are finding the area between the curves you have presented just now?

Answer 40

find the area bounded by the given curves

\[y=\frac{ 1 }{ 2 }(x^2),y=-x^2+6\]

Answer 41

yes freckles

Answer 42

ah, then sketch first

Answer 43

the answer is 16 but how

Answer 44

i dont remember learning this one

Answer 45

do you know how to find the intersections of the equations?

Answer 46

that would be my first step

Answer 47

isn't that where you make them equal each other?

Answer 48

so for example

Answer 49

and yea a graph would help like fibo suggested

Answer 50

1/2x^2=-x^2+6

Answer 51

multiply both sides

Answer 52

yes

Answer 53

a sketch will help a lot

Answer 54

i did that part, i got 2 points, -2 and 2

Answer 55

but idk what to do next

Answer 56

x= +2 and -2

Answer 57

draw a picture.... I swear you won't regret it

Answer 58

sweetie, during a final exam, i don't have time to draw a graph

Answer 59

why not a lesbesque integral
i'd love to see that here

Answer 60

ya do, I swear

Answer 61

this is a final exam?

Answer 62

no but i have one coming up in 2 days

Answer 63

and i have this problem and another one that i need help on if i want to ace it

Answer 64

so i get two points, -2 and +2, what do i do afterwards?

Answer 65

draw a picture I say again, and it shall make it clear

Answer 66

well i like pictures
but you can plug in a number between the intersections to see which function is greater

Answer 67

freckles thats another thing i dont understand, how do you find the greater function

Answer 68

i think it's -x^2+6?

Answer 69

well first off both of these equations are parabolas not that hard to draw
but
if you absolutely refused to draw a graph
plug in a number between the intersections -2 and 2.
like 0
plug in 0 into 1/2*x^2 and 0 into -x^2+6

Answer 70

A picture is a fantastic way

Answer 71

-x^2+6

cause you're left with 6 lol

Answer 72

whats next?

Answer 73

integrate the difference of the larger-smaller on the interval you found

Answer 74

i don't know why i didn't find out about this website earlier, i love this

Answer 75

so (1/2x^2 )-(-x^2+6)?

Answer 76

well you said the larger was -x^2+6

Answer 77

on that interval -2 to 2

Answer 78

sorry i ment the other way around

Answer 79

(-x^2+6)-(1/2x^2)
integrate that on the interval -2 to 2

Answer 80

(-x^2+6)-(1/2x^2)

Answer 81

what do you mean integrate t hat on the intervale -2 to 2

Answer 82

find the integral of (-x^2+6)-(1/2x^2) on [-2,2]

Answer 83

last question guys

Answer 84

this one is stupid easy but i just need confirmation

Answer 85

y=23/x;y=16 when x=1

Answer 86

lol

Answer 87

hellooo?

Answer 88

whered my geniuses go

Answer 89

hey you seem new around here

Answer 90

let me take a moment to welcome you :) \[\color{green}{\text{Welcome to Openstudy!}}\]
Please limit to one question per thread and you need to close the question to open a new question

Answer 91

yea

Answer 92

ok

Answer 93

do i have to open a new thread for each question

Answer 94

yes because the new questions show up in top of the list and your chances for getting help quick increase
scroll up to the start of the question to close it