Need help estimating an area under a curve

In summary, the conversation is about determining the day when the river reaches a height of 114.4 feet based on a graph showing the rate of increase or decrease over a 9 day period. The suggested method is to estimate the area under the curve using rectangles, and it is acknowledged that having access to the raw data would allow for more accurate calculations.
  • #1
viciousp
51
0

Homework Statement


The graph is the graph of the rate of increase or decrease of the river throughout a 9 day period. At day 0 the height is at 111 feet. What day is the river crest at 114.4 feet.

http://img135.imageshack.us/img135/8987/mathgraphoo9.jpg
http://g.imageshack.us/img135/mathgraphoo9.jpg/1/

Homework Equations

3. Attempt at Solution

I know you have to estimate the area under the curve, I used rectangles and got a estimate between the 4th and 5th day. I am just asking if anyone got something similar to that or if I am way off. Thank you in advance
 
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  • #2
If you have the raw data there are a few numerical techniques that can do better ( see Newton-Raphson) but if you just have that chart then the best you can do is to count squares/triangles on paper - for more accuracy you just need smaller squares.
 

1. How do I estimate the area under a curve?

To estimate the area under a curve, you can use different methods such as the trapezoidal rule or Simpson's rule. These methods involve dividing the curve into smaller, simpler shapes and summing their areas to get an estimated value.

2. What is the importance of estimating the area under a curve?

Estimating the area under a curve is important in many fields of science, such as physics, biology, and economics. It allows us to make predictions and understand the behavior of a system or process.

3. Can I estimate the area under any type of curve?

In theory, yes. However, some curves can be very complex and may require advanced mathematical techniques to estimate their area accurately. It is best to use simpler curves or break down complex curves into smaller segments for estimation.

4. What are some limitations of estimating the area under a curve?

One limitation is that the accuracy of the estimation depends on the number of segments used and the chosen method. Using too few segments or an inappropriate method can lead to significant errors. Additionally, estimating the area under a curve is not always possible if the curve is too complex or if there is insufficient data.

5. Are there any tools or software available for estimating the area under a curve?

Yes, there are many tools and software programs that can help with estimating the area under a curve. Some common ones include Microsoft Excel, MATLAB, and Wolfram Alpha. These tools allow you to input your data and choose a method for estimation, making the process more efficient and accurate.

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