r - Calculate the Area under a Curve -

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i calculate area under curve integration without defining function such in integrate().

my data looks this:

date          strike     volatility 2003-01-01    20         0.2 2003-01-01    30         0.3 2003-01-01    40         0.4 etc.

i plotted plot(strike, volatility) @ volatility smile. there way integrate plotted "curve"?

the auc approximated pretty looking @ lot of trapezium figures, each time bound between x_i, x_{i+1}, y{i+1} , y_i. using rollmean of zoo package, can do:

library(zoo)  x <- 1:10 y <- 3*x+25 id <- order(x)  auc <- sum(diff(x[id])*rollmean(y[id],2))

make sure order x values, or outcome won't make sense. if have negative values somewhere along y axis, you'd have figure out how want define area under curve, , adjust accordingly (e.g. using abs() )

regarding follow-up : if don't have formal function, how plot it? if have values, thing can approximate definite integral. if have function in r, can calculate definite integrals using integrate(). plotting formal function possible if can define it.


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