Error in integrate

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Hi!

I am a beginner of R. I am trying to calculate integrate and draw a 
graph of the output, but just kept on getting error messages. I list my 
program and error message below. Please help. Many Thanks!

=======================
+ > a<--11
b<-0.1
c<-0.012
x<-0:110
This is harmless but suspicious -- this x is completely unrelated to the x 
in integrand()
t<-0:15
integrand<-function(x) {exp(-exp(a-c*t)*(exp(b*x)-exp(c*x))/(b-c))}
The problem is that x is a vector of whatever length integrate() decides 
to pass, but t is a vector of length 16.  This mismatch of lengths is 
going to cause a problem.
cal<-integrate(integrand,0,Inf)
Error in integrate(integrand, 0, Inf) : evaluation of function gave a result of wrong length
In addition: Warning message:
longer object length
       is not a multiple of shorter object length in: -exp(a - c * t) * (exp(b * x) - exp(c * x))
plot(cal~t, xlab="Time", ylab="Pop at t")
Error in model.frame(formula, rownames, variables, varnames, extras, extranames,  :
       invalid variable type
===========================

- Vivien Chen -
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