Integration inside a root-find function

Question

I am trying to code a root finding algorithm in R that will solve an equation of the form:

integral from xinitial->x of f(x) = a

with inputs of xinitial, a and the form of function f(x).

Do I need to use vectorize to set up the integral values prior to running them through the root finding algorithm?

Example: y=x x1=1 a=2 I was trying to set up the root find to output the value of x2 at which the integral, ((x2^2)/2 )=a+(x1^2)/2.

Tried using

a<-1.5  
ftn<-function(x)return(x)  
f<-function(x)return(-a+integrate(ftn,1,x)$value +0)  
uniroot( f, c(0, 4) )    

Answer 1

ftn <- function(x) return(x)  
f <- function(x) return(-a+integrate(ftn, x1, x)$value)  
uniroot(f, c(0, 4))