Beginner Python: Division in a while loop-CodePudding

My goal here is to repeat this code using .01 as the base, then .001, and so on 6 times. Using a while loop, how could I run the code once with .01 as the base then divide it 10? How could I repeat that process 6 times? I tried using the /= operator but I get a syntax error.

print("Computing the area under the curve x^2   x   1")
a = int(input("Enter the left end point a: x = "))
b = int(input("Enter the left end point b: x = "))
    
base = 0.1
x = a 
total_area = 0
    
while a <= x and x <= b:
        area = (x**2   x   1) * base
        x  = base
        total_area  = area
    
print("Area under the curve between 40 and 60 using dx =", '{:.0E}'.format(base) , '{:.6f}'.format(total_area))

CodePudding user response：

A for-loop alternative:

print("Computing the area under the curve x^2   x   1")
a = int(input("Enter the left end point a: x = "))
b = int(input("Enter the left end point b: x = "))
    
base = 0.1
iterations = 6

for i in range(iterations):
    total_area = 0
    x = a
    
    while a <= x and x <= b:
            area = (x**2   x   1) * base
            x  = base
            total_area  = area
    
    print("Area under the curve between 40 and 60 using dx =", '{:.0E}'.format(base) , '{:.6f}'.format(total_area))
    base /= 10

CodePudding user response：

You can use an outer while loop that repeats your code 6 times:

print("Computing the area under the curve x^2   x   1")
a = int(input("Enter the left end point a: x = "))
b = int(input("Enter the left end point b: x = "))

count = 0
base = 0.1
while count < 6:
  x = a 
  total_area = 0
      
  while a <= x and x <= b:
          area = (x**2   x   1) * base
          x  = base
          total_area  = area
      
  print("Area under the curve between 40 and 60 using dx =", '{:.0E}'.format(base) , '{:.6f}'.format(total_area))
  base /= 10
  count  = 1

We initialize base as 0.1, and count, the iteration we are on, as 0. We use a while loop to repeat the remaining code until count is equal to 6. In other words, the code doing the Riemann Sum is repeated while count is less than 6. At the end of each iteration, we divide base by 10 and increase count by 1 to move onto the next iteration.

The output to the code is:

Computing the area under the curve x^2   x   1
Enter the left end point a: x = 1
Enter the left end point b: x = 2
Area under the curve between 40 and 60 using dx = 1E-01 4.635000
Area under the curve between 40 and 60 using dx = 1E-02 4.813350
Area under the curve between 40 and 60 using dx = 1E-03 4.838333
Area under the curve between 40 and 60 using dx = 1E-04 4.833833
Area under the curve between 40 and 60 using dx = 1E-05 4.833313
Area under the curve between 40 and 60 using dx = 1E-06 4.833338

And let's check to see if this answer is right:

∫(x^2 x 1)dx from 1 to 2 = (x^3/3 x^2/2 x) from 1 to 2 = (8/3 2 2) - (1/3 1/2 1) = (8/3 4) - (5/6 1) = 20/3 - 11/6 = 29/6 = 4.833 -> our answer is right!

I hope this answered your question! Please let me know if you have any further questions/clarification :)