Area under a graph...

[faredcarsking123]

When you get the area beneath a graph, for example a log graph from x=3 to x=6, is the only the area that is bound by the x-axis, the graph and the lines x=3 and x=6?


What about for two graphs then, like Q1a-iv) in the 2010 Exam 2 VCAA

It just says the area enclosed between the 2 graphs, does that mean we should get the positive part, get the negative part, change the sign and add them or do we just do anti derivative of (top - bottom) over the interval of the whole thing?

[Robert123]

For area between two curves, you do the integral of top-bottom but you use the intercepts as the terminals.

For your first part, I think you are on the right track but when in doubt, graph it first then see where the area is located.

Does that clarify it for you? Your question seems a bit vague so I'm not sure what you are after

[faredcarsking123]

For area between two curves, you do the integral of top-bottom but you use the intercepts as the terminals.

For your first part, I think you are on the right track but when in doubt, graph it first then see where the area is located.

Does that clarify it for you? Your question seems a bit vague so I'm not sure what you are after

Can you please look at 2010 vcaa exam 2 Q1aiv?

They did top-bottom over the interval of where both graphs intersect

My question is do we have to separate the graphs since some of it is below the x-axis, or do we simply calculate the whole thing?

[Robert123]

Can you please look at 2010 vcaa exam 2 Q1aiv?

They did top-bottom over the interval of where both graphs intersect

My question is do we have to separate the graphs since some of it is below the x-axis, or do we simply calculate the whole thing?

Ok now I see what you are asking.
For area between two curves, you can essentially ignore where the x-axis is since it is still top - bottom with the terminals as the intercepts.

Interestingly, when finding the area between a curve and the x-axis, you can approach it the same way as area between two curves as it would be the integral of f(x)-0 (the 0 part is the equation of the x axis). So the area is still equal to the integral of top-bottom.
Does that clarify it for you?

[faredcarsking123]

Ok now I see what you are asking.
For area between two curves, you can essentially ignore where the x-axis is since it is still top - bottom with the terminals as the intercepts.

Interestingly, when finding the area between a curve and the x-axis, you can approach it the same way as area between two curves as it would be the integral of f(x)-0 (the 0 part is the equation of the x axis). So the area is still equal to the integral of top-bottom.
Does that clarify it for you?

Ahh yes thank you!

One last thing

If we have a cosine graph for a length of one period and it says find the area bound by the graph and the x-axis, do we only get the area of the middle as the 2 sides aren't bound by the x-axis?

E.g if the period was 2pi, then from the interval 3pi/2 to pi/2?

[Robert123]

Ahh yes thank you!

One last thing

If we have a cosine graph for a length of one period and it says find the area bound by the graph and the x-axis, do we only get the area of the middle as the 2 sides aren't bound by the x-axis?

E.g if the period was 2pi, then from the interval 3pi/2 to pi/2?

If  the question States "find the area BOUNDED by the curve and the x-axis" then yes, you would do what you said. Otherwise, it depends about how the question is worded. What they generally do is provide a graph with the area you need to find shaded to remove ambiguity.