format long ;
%% sec 2.1 problem 1
f = @(x)(1/sqrt(1+x^4))
I1 = trapezoidRuleUniformGrid(f,0,1,1/8) % I1 = 0.92611518015843

%% sec 2.1 problem 5
g = @(x)x^3
I5 = trapezoidRuleUniformGrid(g,0,1,1/4) % I5 = 0.26562500000000

%% sec 2.1 problem 4 This is the case of non uniform grid
fun = @(x)sin(x)
I4 = trapezoidRuleUniformGrid(fun,0,2*pi/5,pi/5) + ...
    trapezoidRuleUniformGrid(fun,2*pi/5,pi/2,pi/10) % I4 = 0.97457082348881
    %notice that I took h=pi/10=pi/2-2*pi/5 in the second integral