1. Linear Approximation Of Exponential Function

Jul 09, 2011  If you still want to stick to Excel and stay away from apo__1's suggestions, replace the references to +/- infinity with numbers where the function is (nearly) zero or (nearly) 1. For example, with the normal distribution, -6 sigma to +6 sigma is probably a good enough approximation for -infinity and +infinity. Petroleum Engineering 620 — Fluid Flow in Reservoirs Homework 2 — Exponential Integral Function. You are to use the data in the attached Microsoft Excel file.

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Finding the area under a curve is a central task in calculus. This process is called finding the definite integral. Microsoft Excel does not have native calculus functions, but you can map your data to a trendline. Then, once you know the equation of this trendline, you can find the integral. This requires some basic calculus facility -- you must be able to integrate an equation and evaluate it at the beginning and end points.

1.

Select the data set for which you wish to calculate area under a curve.

2.

Click the 'Chart Elements' button in the upper right of the chart. This looks like a large plus sign.

3.

Check the box next to 'Trendline.' Then, click the arrow next to 'Trendline' and select 'More Options' to open the trendline formatting options box.

4.

Select the type of function that best matches the behavior of your data set. You can choose from among Exponential, Linear, Logarithmic, Polynomial, Power and Moving Average functions.

5. Canon mp258.

Check the box next to 'Display Equation on chart.' This will allow you to view the equation so that you can integrate it.

6.

Find the integral of the equation of the trendline. Most of the equation types in Excel have relatively straightforward integration processes. You can think of the integral as the opposite of the derivative. For example, the integral of a linear equation such as f(x)=3x is F(x)=(1/2)3x^2 + c. The new constant, c, will cancel out when you evaluate it. See Resources for some information about integration.

Linear Approximation Of Exponential Function

7.

Evaluate the integral at the upper and lower limits of the desired region. For example, if you want to evaluate the function between x=3 and x=7: F(3) = (1/2)3(3^2) + c = 27/2 +c and F(7) = (1/2)3(7^2) + c = 147/2 + c.

8.

Subtract the integral at the lower limit from the integral at the upper limit to get the total area under the plotted curve. For example, for the above function: F(7) - F(3) = (147/2 + c) - (27/2 + c) = 120/2 = 60.

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