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The process of determining the area under a curve using R involves the following steps:

1. Load the necessary R packages, such as "ggplot2" and "stats".
2. Set up the function or equation for the curve.
3. Create a data frame with a range of x-values for the curve.
4. Use the function or equation to calculate the y-values for the curve.
5. Create a plot of the curve using "ggplot2" or other plotting functions in R.
6. Use the "integrate()" function in R to calculate the area under the curve between two x-values or over the entire range.
7. Interpret and use the result as needed.