# L-25 MCS 471 Wed 19 Oct 2022 : comptrap.jl

using Printf

"""
Applies the composite trapezoidal rule to approximate the integral
of the function f over the interval [a,b], using n subintervals.

Example: t = comptrap(cos,0,pi/2,100)
"""
function comptrap(f::Function,a::Float64,b::Float64,n::Int64)
    h = (b-a)/n
    t = (f(a) + f(b))/2
    for i = 1:n-1
        t = t + f(a+i*h)
    end
    t = t*h
    return t
end

"""
Applies the composite trapezoidal rule
to the area under the unit circle.
"""
function main()
   f(x) = sqrt(1 - x^2)
   exact = pi/4
   N = 1
   for i=1:21
       t = comptrap(f,0.0,1.0,N)
       strnbr = @sprintf("%7d", N)
       strval = @sprintf("%.16e", t)
       strerr = @sprintf("%.2e", abs(t-exact))
       println(" $strnbr  $strval  $strerr")
       N = 2*N
   end
end

main()