Question

Our function is \[\Large{f(x):=x^{3}-7x+6}\]
Determine the area \[\Large{[-2, 2]}\] from the function graph respect to x-pivot

Answer 1

i think they want the integral from -2 to 2

the integral is the area under the graph.

do you have the answer too?

Answer 2

hmm yes it is \[\Large{25\frac{1}{2}}\]

Answer 3

Sei \[\Large{f:\mathbb{R}\rightarrow\mathbb{R}}\] mit \[\Large{f(x)=x^{3}-7x+6}\] Ermitteln Sie den Flächeninhalt der auf \[[-2,2]\] von Funktionen und \[x-Achse\] eingeschlossen wird

Answer 4

i see. it is asking for surface area. which would be the area of the shape obtained if we revolve the function about the x-axis.

\[S = 2 \pi \int\limits_{}^{} f(x) dS\]\[dS = \sqrt{1 + \left( \frac{ dy }{ dx } \right)^2} dx = \sqrt{1 + f'(x)^2} dx\]

Answer 5

hmm

Answer 6

Euler could you pls solve it , if u can it would be much appreicated, i have exam on wendsday

Answer 7

if it's actually looking for surface area, this particular problem is very hard. i wouldn't know how to integrate it.
i'm actually not convinced they want surface area, since i used a translator.

sorry that i can't help more. hopefully somebody german can decrypt what the question is really asking for

Answer 8

ok Euler thanks anyway for your patience

Answer 9

here smilar question maybe you would like to take a look on it http://maleroh.de/uebungsaufgaben - mathe.htm

Answer 10

the link doesn't work

Answer 11

@tunahan

Answer 12

sorry

Answer 13

i will find wait pls

Answer 14

third one https://www.google.de/?gws_rd=cr&ei=LvlSUrjnH4nHswait4CgCg#q=Sei+f:R →R+mit+f(x)=x3−7x+6+Ermitteln+Sie+den+Flächeninhalt+der+auf+[−2,2]+von+Funktionen+und+x−Achse+eingeschlossen+wird

Answer 15

i am sorry :( it doesnt work too..

Answer 16

http://maleroh.de/uebungsaufgaben - mathe.htm if u copy this link until end of .... mathe.htm and paste it in browswer it works

Answer 17

it works :)

which number(s) are examples of it?

Answer 18

it starts like that ******Berechnen Sie die Maßzahl des Flächeninhaltes der Fläche, welche vom Graphen der Funktion f mit der Gleichung : f(x) = x² - 5x + 4 , der x-Achse sowie den senkrechten Geraden x1 = 0 und x2 = 4 eingeschlos- sen wird!*****

Answer 19

ohhhhhhhhhh

Answer 20

actually i think i understand but the only thing that i dont understand is how to determine between [0, 4] 1 to 0 and 4 to 1 without graph

Answer 21

with graph i can see it but without i dont know how to..

Answer 22

http://www.wolframalpha.com/input/?i=x%5E3+-+7x+%2B+6

from this graph, you can see that the function goes below the x-axis between 1 and 3. this naturally results in subtraction if you take up the straight up integral. so you want the "real" area so you take those places into account and make sure they are added instead of naturally subtracted.

you will need to graph it to figure it out. you can also do a few tests to deduce

Answer 23

if you find the roots (the values of x where f(x) = 0), you can test a number in between the roots to figure out if they are above or below the axis

Answer 24

ooh ok i get it thank you very much Euler =) its much apreciated, now the only thing is to practise it until exam =)

Answer 25

glad i could help :)