```
# Calculate the area under the sine curve from 0 to pi:
n <- 101
x <- seq(0, pi, len = n)
y <- sin(x)
trapz(x, y) #=> 1.999835504
# Use a correction term at the boundary: -h^2/12*(f'(b)-f'(a))
h <- x[2] - x[1]
ca <- (y[2]-y[1]) / h
cb <- (y[n]-y[n-1]) / h
trapz(x, y) - h^2/12 * (cb - ca) #=> 1.999999969
# Use two complex inputs
z <- exp(1i*pi*(0:100)/100)
ct <- cumtrapz(z, 1/z)
ct[101] #=> 0+3.14107591i
f <- function(x) x^(3/2) #
trapzfun(f, 0, 1) #=> 0.4 with 11 iterations
```

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