Find the area under this graph by integration (it's a simple function)

In summary, the conversation is about finding the area between two given values on a graph using integration. The function is y= 360(1.0297^x) and the points are provided. The conversation also mentions using methods like Trapazoidal Approximation and Simpson's Rule to approximate the area, but one person suggests using a substitution to solve the integral instead.
  • #1
Eutrophicati
10
0

Homework Statement



This is the function:
y= 360(1.0297^x)
Find the area between x=24, and x=48.
The graph looks like this: http://tinypic.com/r/30w4bjp/5

And the points are:
24, 740.8379
30, 883.0544
36, 1052.572
42, 1254.631
48, 1495.479

ASAP svp. =]

Homework Equations


Ah... You know it =/
http://upload.wikimedia.org/math/8/1/9/819ac78e8461a8a9c55f3f845e577620.png

The Attempt at a Solution


Unfortunately, I haven't learned integration. But I'm working on a Math IA (Internal Assessment) and I want to do this with a slightly higher quality. I just did some research but it's Greek to me so far =/
Can someone calculate this please? I'd like to see maybe 2 or 3 steps to try and understand how you did it.
 
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  • #2
If you don't know integration, do you know any method to approximate the area? It will make no sense to try to explain the integration to you if you don't know what integration is in the first place.
 
  • #3
well I got 25299.6908 with Trapazoidal Approximation and 25105.80447 using Simpson's Rule but I can not tell you the error rate on either number because I don't know how to take the derivatives of that function. Contrary to what you might think it is not an elementary function. I can tell you that the number using Simpson's Rule is closer to the actual result than the trapazoidal approximation but I can't tell you how close...

I got those using dx = 2, so if i took a smaller dx it would be better as well, but I don't want to spend the time doing all those calculations...
 
  • #4
Asphyxiated said:
Contrary to what you might think it is not an elementary function.

Actually, that integral can be solved using a substitution.
 
  • #5
really? I tried that but i couldn't get anything to come out, what is the substitution then? what does u =?
 

1. What is integration and why is it used to find the area under a graph?

Integration is a mathematical process used to find the total area under a curve on a graph. It involves breaking the curve into small, infinitesimally thin sections and summing up the areas of these sections. Integration is used to find the area under a graph because it allows for precise and accurate calculations, even for complex curves.

2. How do you perform integration to find the area under a graph?

To perform integration, you first need to determine the function that represents the curve on the graph. Then, you use integration rules and techniques to find the antiderivative of the function. The antiderivative is a new function that represents the original function's area under the curve. Finally, you can use this antiderivative to calculate the area under the graph at specific points or over a specific interval.

3. Can integration be used for any type of graph or function?

Yes, integration can be used for any type of graph or function as long as the function is continuous, meaning it does not have any sudden breaks or jumps. If the function is not continuous, then integration cannot be used to find the area under the graph.

4. What are some real-world applications of using integration to find the area under a graph?

Integration is used in many fields, including physics, engineering, and economics. It can be used to find the displacement of an object over time, the work done by a force, or the profit generated by a business. In biology, integration can be used to calculate the rate of change of a population over time. In essence, integration is a powerful tool for understanding and analyzing real-world phenomena.

5. Are there any limitations or challenges when using integration to find the area under a graph?

One limitation of integration is that it can be challenging to find the antiderivative for complex functions. This requires a good understanding of integration rules and techniques. Additionally, integration may not always be the most efficient method for finding the area under a graph, especially for functions with sharp turns or multiple curves. In these cases, other methods such as numerical integration may be more suitable.

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