area between curves...sos! (1 Viewer)

[ryanox]

question 4 (c) in 2003 hsc is about area between curves.
(i) says 2 find the coordinates of A which was found 2 b (1,-3)
(ii) syas "find the area of the shaded region bounded by y=x^2-4x and y=x-4." the x ooridanates are (1) and (4).

how do u kno which function to take away from the other??

 

[roosterman]

the answer says its (x-4) - (x^2-4x).

but im confused as well!

 

[SoulSearcher]

In this case it's the parabolic function subtracted from the linear function, i.e. x - 4 - (x² - 4x). Normally, whichever function borders the top of the area is the function which the other function is subtracted from.

 

[roosterman]

How did you know?
Its confusing because isnt the area between the x-axis and the parabola be more then the line and the x-axis.

 

[SoulSearcher]

There is no difference in the area between the curves if you shifted it up above the x-axis, if the area between the curves was entirely above the x-axis, then the area between the parabola and the x-axis would be less than the area between the straight line and the x-axis. There is no difference, that is why you take the upper function and subtract the lower function from it in the majority of cases.

 

[roosterman]

cool