4.7. Python Code Example (Trapezoidal Rule)

Try these first

1. 1.

   What does the trapezoidal rule approximate?

   Hint

   Think of how this relates to shapes we know.

2. 2.

   Define a function in Python that squares its input.

   Hint

   What does x represent in programming?

3. 3.

   What type of shape does the trapezoidal rule use for approximation?

   • Triangles
   • Trapezoids
   • Rectangles

   Hint

   Think about the name of the rule.

4. 4.

   True or False: The trapezoidal rule can be used for functions with discontinuities.

   • True
   • False

   Hint

   Consider how discontinuities might affect the shapes involved.

5. 5.

   Using the trapezoidal rule, approximate the integral of f(x) = sin(x) from 0 to π using 10 intervals.

   Hint

   Consider how the sine function behaves across this interval.

6. 6.

   Create a Python function using the trapezoidal rule to approximate the integral of f(x) = e^x from 0 to 1 with 20 intervals. Discuss the results.

   Hint

   Make sure to calculate the heights of the function correctly at intervals.