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3 cards from this section. Quick, good the night before a test.
What is the main purpose of numerical integration?
Think about scenarios where exact answers are hard to find.
Name a numerical method used in numerical integration.
These methods are named after mathematicians.
What is the main application of numerical integration?
Consider what numerical methods are designed for.
True or False: Simpson's Rule can be used only if the number of intervals is odd.
Think about the requirements for applying Simpson's Rule.
Suppose you have a force function acting on a vehicle, F(x) = 3x^2 - 5x + 2. Calculate the work done by this force over the interval [1, 3] using the Trapezoidal Rule with n=4.
Calculate stepwise according to the trapezoidal formula and integrate accurately.
Imagine modeling the population growth of a bacteria colony with the differential equation dP/dt = 0.03P(1 - P/400) where P is the population. Use numerical integration to estimate the population after 10 days starting with P(0) = 50 using Simpson's Rule.
Focus on setting up the time intervals and using the growth rate as the function for integration.
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