skyindeer - 4 months ago 67

R Question

I want to compute a 2-fold repeated integral (not double integral) in R, for example,

where

In practice, both f(x) and g(x) are quite complicated, but to run an experiment, let's simplify g(x)=1 and f(x)=cos(x), in R I use

`integrate`

`> phi = function(x){integrate(function(x){cos(x)},lower=x,upper=3)[["value"]]^2}`

> foldintegral = integrate(phi,lower=0,upper=3)

And I got this error message:

`Error in integrate(phi, lower = 0, upper = 3) :`

evaluation of function gave a result of wrong length

Any Idea how to do that ?

Answer

All that is needed is

```
integrate(Vectorize(phi), lower=0, upper=3)
# 1.067943 with absolute error < 1.2e-14
```

Compare

```
phi(1)
#[1] 0.4904915
phi(1:3)
# [1] 0.4904915
Vectorize(phi)(1:3)
# [1] 0.4904915 0.5900965 0.0000000
```

`integrate`

expects a vectorized function.