7-7 Approximate Integration.sagews

# Left endpoints
f(x) = e^(sqrt(x))
a = 0
b = 2
n = 10
((b-a)/n * sum([f(a + (b-a)/n*i) for i in range(0, n)])).n()

5.40596506491409

# Right endpoints
f(x) = e^(sqrt(x))
a = 0
b = 2
n = 10
((b-a)/n * sum([f(a + (b-a)/n*i) for i in range(1, n+1)])).n()

5.70336429687777

# Midpoint Rule
f(x) = e^(sqrt(x))
a = 0
b = 2
n = 10
((b-a)/n * sum([f(a + (b-a)/n*i + (b-a)/(2*n)) for i in range(0, n)])).n()

5.41143281809145

# Trapezoid Rule
f(x) = e^(sqrt(x))
a = 0
b = 2
n = 10
((1/2)*(b-a)/n * (f(a) + 2*sum([f(a + (b-a)/n*i) for i in range(1, n)]) + f(b))).n()

5.39203925899948

# Simpsons Rule
f(x) = e^(sqrt(x))
a = 0
b = 2
n = 10
((1/3) * (b-a)/n * (f(a) + 4*sum([f(a + (b-a)/n*i) for i in range(1, n, 2)]) + 2*sum([f(a + (b-a)/n*i) for i in range(2, n, 2)]) + f(b))).n()

5.40030868489391

numerical_integral(e^(sqrt(x)), 0, 2)

(5.407528209144933, 4.319742265069264e-06)