%% Script file for Computer Problem 5.2.7

%% f(x)=x^2
f=inline('x.^2');
M=2.^[0:16];
k=length(M);
for j=1:k
    A(j)=comptrap(f,0,1,M(j));
end
figure(1)
x=log(1./M);
plot(x,log(abs((1/3)-A)),'r*',x,2*x-1.8,'b-')
title('Area for x^2')

%% f(x)=cos(x)
f=inline('cos(x)');
M=2.^[0:16];
k=length(M);
for j=1:k
    A(j)=comptrap(f,0,pi/2,M(j));
end
figure(2)
x=log((pi/2)./M);
plot(x,log(abs(1-A)),'r*',x,2*x-2.5,'b-')
title('Area for cos(x)')

%% f(x)=cos(x)
f=inline('exp(x)');
M=2.^[0:16];
k=length(M);
for j=1:k
    A(j)=comptrap(f,0,1,M(j));
end
figure(3)
x=log(1./M);
plot(x,log(abs((exp(1)-1)-A)),'r*',x,2*x-1.9,'b-')
title('Area for exp(x)')