R plotting integral

Question

I'm having some problems with integration function in R. I'm trying to plot the integral vo but it seems I'm not doing correctly.

t <- seq(0, 0.04, 0.0001)
vi <- function(x) {5 * sin(2 * pi * 50 * x)}
vo <- function(x) {integrate(vi, lower=0, upper=x)$value}

test_vect = Vectorize(vo, vectorize.args='x')
plot(t, vo(t))  # should be a cosine wave
plot(t, vi(t))  # sine wave

vo should be a sine wave but using test_vect gives me wrong plot and using vo directly gives error 'x' and 'y' lengths differ. Can anyone, please, help me on this matter?

Answer 1

You are already there. Just use plot(t, test_vect(t)). You can't use vo, as integrate is not a vectorized function. There is no problem to evaluate a single point like vo(0.002), but you can not feed it a vector by vo(t). This is why we want Vectorize(vo)(t).

You said that test_vect is not giving the right plot. Sure? We can analytically compute the integral:

v <- function (x) (1-cos(100*pi*x)) / (20*pi)

Then let's compare:

sum(abs(v(t) - test_vect(t)))
# [1] 2.136499e-15

They are the same!