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4 cards from this section. Quick, good the night before a test.
What is the Trapezoidal Rule used for?
Think about the shape used in the calculation.
What must be true about the function f(x) for numerical integration?
Consider the behavior of f(x) in the given interval.
What does numerical integration approximate?
Focus on the purpose of numerical methods.
True or False: The Trapezoidal Rule can only be used on linear functions.
Think about the flexibility of this rule.
Given the function f(x) = sin(x) on the interval [0, π] with n = 4, calculate the approximate integral using the Trapezoidal Rule and discuss the expected versus actual error.
Remember, calculate values for the function, and estimate second derivatives.
Using Simpson's 3/8 Rule, approximate the integral of f(x) = e^x from 0 to 1 with n = 3 intervals, and evaluate the accuracy compared to an exact solution.
Identify function values at required points to compute the approximation.
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