Question

Area Under A Curve

What formula's so I need/use for this worksheet ?

Answer 1

which problem exactly?

Answer 2

all of them ,
i just want to know which formula's i need to use so that i can solve them all .

Answer 3

first of all find the critical points i.e. dy/dx=0 then proceed further when the slope is +ve or -ve between those intervals

Answer 4

r u from india?

Answer 5

no

Answer 6

ok...any other questions?

Answer 7

why would you need critical points for this problem...? it's one of those rectangle approximating things that everyone hates lol

Answer 8

everyone hates ? :)

Answer 9

I thought critical points could help in drawing the graph...could be wrong..

Answer 10

who needs to approximate when you can just integrate :P i always just do it and forget it

Answer 11

id say integrate really :)

Answer 12

why learn to walk if you are running marathons?

Answer 13

wait...so what am i supposed to do :O

Answer 14

you are supposed to learn that doing it the long and tedious way is proof that the shortway is better....

Answer 15

im not running marathons im barely even walking lol

Answer 16

when you have a function that is difficult to integrate, you can approximate the area under its curve thru numerical stuff like the trapaziod rule or simpsons rule and other time consuming methodss

Answer 17

but these? really? lol

Answer 18

what do you mean but these?

i dont understand anything yo u just said /:

Answer 19

[S] -x^2 +4 dx [0,2]

F(x) = -x^3/3 + 4x ....at 0 its useless so solve for 2

-8/3 + 12 = -8 +36//3 = 28/3

Answer 20

and I mess up doing simple multiplication lol....4(2) = 8 ;)

Answer 21

-8/3 +8 = -8 +24//3 = 16/3....maybe :)

Answer 22

integrating isnt the answer she wants though

Answer 23

its the answer, just not the "way" :)

Answer 24

you wont get teh same answer by approximating

Answer 25

you will if you take the reaimann sums and sll that fun stuff...right? if I recall correclt?

Answer 26

with inscribed and ourscribed rectangles you get the average and yadayada...

Answer 27

yeah but reimann sum is taking an infinite number of rectangles, this is just like a few boxes

Answer 28

then lets do boxes ;) we have to do it inscribed and outscribed.. but Im pretty sure you end up with the average being the limit of the 2..

Answer 29

mean value theorum or some such....

Answer 30

y'all are confusing mee /:

Answer 31

y = -x^2 + 4 find your f(x) values for your little rectangles.... do left right sides

Answer 32

y = -.5^2 + 4

y = -1^2 + 4

y = -1.5^2 + 4

y = -2^2 + 4

Answer 33

the area of each "rectangle" is gonna be .5 * its y value

Answer 34

then add the areas up

Answer 35

I can draw a picture if you like :)

Answer 36

yes please

Answer 37

like this

Answer 38

each place a corner touches the curve; we get a value for y right?

Answer 39

\: im still confused .
i guess i got lost along y'alls "discussion" ..

Answer 40

do you see the rectangles I drew? they have a width and a height right?

Answer 41

yes

Answer 42

the right edge of each rectangle hits the curve...and stops because we drew if INside the curve.... inscribed

Answer 43

we are told that we do this every .5 units..... so the width of each rectangle is .5 makes sense?

Answer 44

yes

Answer 45

good, then all we need to figure out the area of any given rectangle is ...we already now its width (.5) is going to be its height...right?

Answer 46

yep

Answer 47

so at the first interval where x = .5; we go up until we hit the curve of y = -x+4

sine the value of "y" is our height we need to use the equation to figure out the height at x = .5

y = -.5^2 + 4
y = -2.5 +4

y = 1.5 is this right?

Answer 48

like this

Answer 49

and of course I forgot how to square decimals...... -(.5*.5) = -.25

4-.25 = 3.75 thats better

Answer 50

revised and corrected version lol

Answer 51

at our next step, .5 + .5 = 1. we stick x = 1 into our equation to get the height for the second rectangle; width = .5 and height =-x^2 +4.

h = -(1^2) + 4
h = -1 + 4
h = 3

Area2 = .5 * 3 = 1.5

Answer 52

this would be easier if I didnt keep getting typos..... this is right.

Answer 53

at our next step, .5 + .5 +.5 = 1.5 we stick x = 1.5 into our equation to get the height for the third rectangle; width = .5 and height =-x^2 +4.

h = -(1.5^2) + 4
h = -2.25 + 4
h = 1.75

Area3 = .5 *1.75 = .875

Answer 54

at our next step, .5 +.5 +.5+.5 = 2 we stick x = 2 into our equation to get the height for the third rectangle; width = .5 and height =-x^2 +4.

h = -(2^2) + 4
h = -4 + 4
h = 0

Area4 = .5 *0 = 0 Do we really need to include this one? lets assume no :)

Answer 55

Now we add up all the areas of our rectangles:

A1 + A2 + A3 + A4 = answer

1.875 + 1.5 + .875 + 0 = answer

1.875 + 1.5 + .875 + 0 = 4.25 this is the smallest value for the area under the curve that is reasonably close to the actual area under the curve.

Any of this make sense?

Answer 56

if any of this doesnt make sense.....let me know.

Answer 57

im sorryy if i'm making you impatient but my mind is VERY blank right now /:

Answer 58

im not impatient dear :) just wanting to help you see what you really already know ;)

Answer 59

tell me what you are having trouble with...and I can explain it better for you.