Question

how do you find the area between two curves?

Answer 1

integrate between them

Answer 2

how do you do that?

Answer 3

lets turn the curves into lines...straight horizontal lines and see what happens :)

Answer 4

if we bind them between x=0 and some other value like x=10 we get a square or rectangle shape right?

Answer 5

yes yes

Answer 6

like this; how would we determine the area of the orange part?

Answer 7

we would take the area of the whole thing from the x axis to the top "function".

and subtract the area that is defined by the x axis to the bottom "function"....right?

Answer 8

Total area - grey area = orange area...

Answer 9

yes yes

Answer 10

How do you find the upper function?

Answer 11

the upper function tends to be defined; they give you 2 curves and say find the area between them right?

Answer 12

if you dont know the "upper" function off hand, just pick one; and if your area is negative, then you choose the wrong one :)

tell me: does:

5-8 = -3?

8-5 = 3?

same numbers, different order just produce a spurious (-)

Answer 13

if you decide to take the absolutle value of whichever way you do:

|-3|

then it really doesnt matter :)

Answer 14

If the whole are is 10, and the part to take away is 4:

10-4 = 6 which is correct. but if you switch them its no big deal really since area is not negative to begin with.

4 - 10 = -6 gives an area, its just been done backwards...|-6| is what you want

Answer 15

does that make sense?

Answer 16

yes yes (:

Answer 17

so you just guess and check to find which one is the upper function?

Answer 18

and then once you have found it, you subtract it from the lower function?

Answer 19

if you cant tell the difference between the two, then yeah :) Youll know your backwards when you get a (-) area between two curves because thats just silly :) tell me, between me and you is there negative distance?