Just need a quick explenation ! ( Integrals)

[ArthurJ]

∫_a^b▒〖f(x)-g(x)〗  , so I understand that this will give me the area between two curves between two certain points.

However, I’m just unsure as to how I deal with problems that go under the x axis. I don’t seem to get the right answer, is it because it’s a negative area?
If so do I just do -∫_a^b▒〖f(x)-g(x)〗  ?
We only learnt it today, but yea any help would be much appreciated!

[ArthurJ]

the _a^b▒ was ment to be the upper bound and lower bound but my icon stuff is playing up :/

[Alwin]

∫_a^b▒〖f(x)-g(x)〗  , so I understand that this will give me the area between two curves between two certain points.

However, I’m just unsure as to how I deal with problems that go under the x axis. I don’t seem to get the right answer, is it because it’s a negative area?
If so do I just do -∫_a^b▒〖f(x)-g(x)〗  ?
We only learnt it today, but yea any help would be much appreciated!

It doesn't matter whether the graphs of f(x) and g(x) are above, or below the x axis. the only thing that matters is which one is above the other, ie if f(x)>g(x) then do f(x) - g(x) in the integral. Otherwise, if g(x)>f(x) then you must do g(x)-f(x).

What problem were you having difficulty with getting the right answer?

[brightsky]

just memorise the following formula:

area = int^(right bound)_(left bound) (top curve - bottom curve) dx

it's also good to understand why it doesn't matter whether the graphs are below, above or straddling the x-axis. consider all possible cases and work the answer out from 'scratch'.