Need help estimating an area under a curve

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SUMMARY

The discussion focuses on estimating the area under a curve representing the rate of change of a river's height over a 9-day period. The user seeks confirmation on their estimation, which suggests that the river crests at 114.4 feet between the 4th and 5th day. Techniques mentioned include using rectangles for estimation and the Newton-Raphson method for more precise calculations if raw data is available. The consensus indicates that without raw data, the best approach is to refine the estimation by using smaller geometric shapes.

PREREQUISITES
  • Understanding of integral calculus concepts, specifically area under a curve.
  • Familiarity with numerical estimation techniques, including the rectangle method.
  • Knowledge of the Newton-Raphson method for root-finding in mathematical functions.
  • Basic graph interpretation skills to analyze rate of change over time.
NEXT STEPS
  • Research numerical integration techniques, focusing on the Trapezoidal Rule.
  • Learn about the application of the Newton-Raphson method in estimating areas under curves.
  • Explore advanced graphing tools for better visualization of data trends.
  • Study the concept of Riemann sums for more accurate area estimations.
USEFUL FOR

Students in calculus, mathematicians, and anyone involved in data analysis or environmental studies focusing on rate changes over time.

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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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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.
 

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