var('x')
f(x) = sqrt(x)
a=0
b=4
n=20
h = (b-a)/n
ex = integral(f(x),x,a,b)
show('Exact: ',ex.n())
L = h*sum([f(a+k*h) for k in range(n)])
show('Left: ',L.n())
show('Error: ',(ex-L).n())
R = h*sum([f(a+k*h) for k in range(1,n+1)])
show('Right: ',R.n())
show('Error: ',(ex-R).n())
T = .5*(L+R)
show('Trap: ',T.n())
show('Error: ',(ex-T).n())