Area bounded between two curves, choosing curves

In summary, the conversation discusses the process of finding the area bounded between two curves and whether there is a foolproof way to choose which curve to subtract in the integral equation. The speaker also mentions that they have encountered difficulties with this in the past. Ultimately, it is determined that the answer will not be affected by which curve is chosen, as it will only differ by a minus sign.
  • #1
JesseJC
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I don't have a particular problem in mind here, so please move this thread if it's in the wrong section.

I was wondering, when you're trying to find the area bounded between two curves, is there a foolproof way to choose which curve to be g(x) in (let S be the integral sign, haha) S[f(x)-g(x)]dx? Is there a way to tell by looking at the graph?

I've done a few of these problems and choosing which curve to subtract is not always intuitive, to me at least.
 
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  • #2
JesseJC said:
I don't have a particular problem in mind here, so please move this thread if it's in the wrong section.

I was wondering, when you're trying to find the area bounded between two curves, is there a foolproof way to choose which curve to be g(x) in (let S be the integral sign, haha) S[f(x)-g(x)]dx? Is there a way to tell by looking at the graph?

I've done a few of these problems and choosing which curve to subtract is not always intuitive, to me at least.
It really doesn't matter - the two answers that you'll obtain will only differ by a minus sign. Just take the modulus of the answer either way.
 

FAQ: Area bounded between two curves, choosing curves

1. What is the area bounded between two curves?

The area bounded between two curves is the region enclosed by two curves on a graph. It is the area between the two curves and the x-axis.

2. How do I choose which curves to use?

The curves used should be the functions that define the boundaries of the region. These functions should be continuous and intersect at the points where the region begins and ends.

3. Can I use any type of curves?

Yes, any type of curves can be used as long as they meet the criteria mentioned above. This can include linear, quadratic, exponential, trigonometric, or any other type of function.

4. How do I calculate the area bounded between two curves?

The area can be calculated using integration. You can find the points of intersection between the two curves, set up the integral, and evaluate it to find the area.

5. What is the practical use of finding the area bounded between two curves?

Finding the area bounded between two curves is helpful in many fields, such as engineering, physics, and economics. It can be used to calculate the total volume of a shape, determine revenue or profit, or find the distance traveled by an object.

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