Area between two graphs (1 Viewer)

[lolJK]

hi,
you know those questions where it gives you two functions and you have to find the area enclosed between two points of intersection...
How do you find which function is on the top (if you get me?) as in which function do you put first into the integration formula, then minus the other function...can you put any and just absolute value everything?

thanks, let me know if you cant understand what i mean.

 

[Carrotsticks]

If you have a diagram, then it's obvious which curve is above the other.

If you DON'T have a diagram... then you will need to make one or find algebraically which function is higher than which in the domain of integration (more difficult).

 

[Shadowless]

hi,
you know those questions where it gives you two functions and you have to find the area enclosed between two points of intersection...
How do you find which function is on the top (if you get me?) as in which function do you put first into the integration formula, then minus the other function...can you put any and just absolute value everything?

thanks, let me know if you cant understand what i mean.

can we do this? cos i have been...

 

[Sy123]

Yes because:
Lets take the area underneath the curves f(x) and g(x), lets say:

Here we are assuming that f(x) is above g(x) for all the domain in the limits of the integral, now:



So you can absolute value them

 

[barbernator]

Yes because:
Lets take the area underneath the curves f(x) and g(x), lets say:

Here we are assuming that f(x) is above g(x) for all the domain in the limits of the integral, now:



So you can absolute value them

This is also assuming that either function doesn't have some area above and some area below the x axis, in which you would have to split the integrals.