area between functions

[proud forge]

hi if i have this case how can i calculate the area? (we haven’t done integrals yet) It is given only the functions of each graph

[verbal swift]

1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
2. Wait patiently for a helper to come along.
3. Once someone helps you, say thank you and close the thread with:

   +close
   

4. Feel free to nominate the person for helper of the week in #helper-nominations
5. Do not ping the mods, unless someone is breaking the rules.
6. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[boreal cedar]

...so what are the functions then? Like, are we supposed to answer the question just from this... what looks like an MSPaint image?

[open raft]

Bro what are the functions? You want us to measure it?

[proud forge]

bro i meant the procedure to calculate it… not the precise case

[proud forge]

no, just how to do it

[slender tree]

if you integrate wrt to x take the right most function - left
if you integrate wrt y take the top minus bottom function

[proud forge]

i said i can’t integrate

[neon horizon]

i dont think so u can do this without integration

[proud forge]

idk

[slender tree]

how are you going to get the area of a shape like that then...

[proud forge]

i can get the area of the parabolical segment using archimedes theorem

but i would still be missing a part of the total area

[slender tree]

uh ok

[proud forge]

i can get the yellow area with archimede theorem

[slender tree]

ya idk what that is i thought u were talking about the buoyant force in physics lol

[proud forge]

no idea what that is 🤔

[neon horizon]

lol same here

[proud forge]

it basically says that the area of the yellow part is equal to 4/3 of the area of the biggest triangle u can put in the yellow part

this one

[neon horizon]

okay u can get the two base cordinates by solving the curve but how do u know that the area for which third vertex is the max?

[proud forge]

the vertex is obtained by doing the perpendicular to the line creating the yellow part

[neon horizon]

yes but where?

[proud forge]

it’s the axis of the black segment

the vertex is not a problem to find

the real problem is the green part

[neon horizon]

i find this to be the biggest area

[proud forge]

it’s not

[neon horizon]

how do u know for sure?

[proud forge]

there is a theorem that says the biggest area possible is the one with its height being the axis of the segment

[proud forge]

it was proven but we skipped the dimonstration

[neon horizon]

axis of segment? perpedicular bisector u mean?

[proud forge]

well in an isoscel triangle it’s the same thing (?)

[neon horizon]

yeah isocles yeah

[proud forge]

the blue line is the axis of AB

[neon horizon]

so archemeids is sayignt that "for a parabola and circle, the biggest area shaded in yellow is 4/3 of the are of biggest (by area) issocles triangle that can be drawn inside it?"

[proud forge]

no, it says that if u cut a random parabola with a line, you get AB (cord of the parabola). The cord divides the area of the parabola in two parts, one is infinite and the other is limited. The limited part is called “parabolical segment”(in yellow). The biggest triangle u can build inside the parabolical segment has for its height the axis of AB. The area of the parabolical segment is =4/3 of the area of the biggest triangle you built inside of it

[proud forge]

it’s not only for circles

[neon horizon]

oh

i still dont know if axis means like perpendicular bisector is is it somthing else, so like the triangle should be issoscles?

[proud forge]

yea the triangle is isosceles

but that fact isn’t really important

i can calculate the area by doing base x height /2

[neon horizon]

hmm wait lemme think

[proud forge]

alr

[neon horizon]

u can calculate the rest of the area by like joining A, and B to centre and calc the ansgle between them

find the area of segment

= area of sector - area of triangle

= pi. r^2. theta / 360 - 1/2. r^2. sin theta

[proud forge]

oh that’s a good idea