3411.sagews

# 8.6 Number. 17

def f1(input):
    return sin (pi * (input))

# Trapezoid Rule Approximation
# TR = Trapazoid Rule

# Define Variables
n = 6
a = 0   
b = 1
answer = 0
TR = 0

tx = (b - a)/n
for ix in range(n - 1):
    lowt = a + ix*tx
    hight = a + (ix + 1)*tx
    tp = hight
    TR = TR + f1(tp)

answer = ((.5 * f1(a)) + TR + (.5 * f1(b)))*tx
# Answer is one half of f(a) + Sum from 1 to n-1 of the high point (b) + one half f(b) times delta x (tx)

    
# Statement that prints the answer:
print "Answer is approximately: 0.6220084679"
print "Answer Sage gives me is:" 
answer

Answer is approximately: 0.6220084679 Answer Sage gives me is: 1/6*sqrt(3) + 1/3