Signed Area

[Andiio]

If a question asks you to find/calculate the 'signed area' of a curve, is it simply a one-step integration? (i.e. ignoring +/- areas, so finding the magnitude)

[paulsterio]

Yes, its just the integral between the two bounds
It can have a negative value

Also, no, you're not correct in saying finding the magnitude, finding the magnitude is finding the area, here you are NOT finding the magnitude

[abeybaby]

Does signed area have units?

[paulsterio]

Does signed area have units?

well, if you consider that both distance and displacement are measured in meters, and distance is effectively the unsigned area under a velocity-time curve and displacement is the signed area, I think that it's fair to say signed areas would have units?

[abeybaby]

but then would you say something like, the signed area is -5 square units? cos that sounds weird to me...

[BlueSky_3]

Based off a reliable source, signed area does not include units according to VCAA.

[paulsterio]

but then would you say something like, the signed area is -5 square units? cos that sounds weird to me...

you make a good point....hmmm

Based off a reliable source, signed area does not include units according to VCAA.

oh, thanks for that
and btw, what's the source?

[b^3]

but then would you say something like, the signed area is -5 square units? cos that sounds weird to me...

you make a good point....hmmm

Based off a reliable source, signed area does not include units according to VCAA.

oh, thanks for that
and btw, what's the source?

The way I look at it is that signed area does not have units, but when interpretting a problem, in the context of the problem units may be needed, i.e. -5 could be the displacement or velocity, it's just in the opposite direction.

[BlueSky_3]

The source is a certain Dr.G who happens to be an experienced methods and specialist maths teacher at Melbourne High School.

[paulsterio]

The way I look at it is that signed area does not have units, but when interpretting a problem, in the context of the problem units may be needed, i.e. -5 could be the displacement or velocity, it's just in the opposite direction.

Hmm, alright then, I've never really thought about it haha!

and you mean -5 could be the displacement or distance?

The source is a certain Dr.G who happens to be an experienced methods and specialist maths teacher at Melbourne High School.

Oh right then, I guess no units it is

[david10d]

It seems like Dr G and Dr He think alike.

[paulsterio]

It seems like Dr G and Dr He think alike.

Well Geeeeee and Heeeeeee rhyme
G and H are next to eachother in the alphabet
They're both have doctorates in areas of mathematics
They're both acclaimed in the field of maths
They're both known for setting hard questions
LOL! =.=" any more similarities?

[b^3]

The way I look at it is that signed area does not have units, but when interpretting a problem, in the context of the problem units may be needed, i.e. -5 could be the displacement or velocity, it's just in the opposite direction.

and you mean -5 could be the displacement or distance?

Well bringing physics into this, distance is a scalar quantity, displacement, velocity, acceleration are vector quantites, so they have direction associated with them. The signed area will give you displacement not distance as it takes away the area underneath, this is the time when it is travelling in the opposite direction and so will give displacement not distance. To get distance you have to split the intergral up .....blah blah (you know what I mean). With velocity, it will just be the area under a acceleration time graph (although I don't think we get those in methods). The negative velocity, say -5, would mean it is just travelling in the opposite direction.

[paulsterio]

yeah, b^3, I realized that I misinterpreted what you said the first time, my bad

but yeah, that's how I understand it as well, so I guess we're clear on this now