4.6 - Practical Applications
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
What is the main purpose of numerical integration?
💡 Hint: Think about scenarios where exact answers are hard to find.
Name a numerical method used in numerical integration.
💡 Hint: These methods are named after mathematicians.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the main application of numerical integration?
💡 Hint: Consider what numerical methods are designed for.
True or False: Simpson's Rule can be used only if the number of intervals is odd.
💡 Hint: Think about the requirements for applying Simpson's Rule.
Get performance evaluation
Challenge Problems
Push your limits with advanced challenges
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.
💡 Hint: 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.
💡 Hint: Focus on setting up the time intervals and using the growth rate as the function for integration.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.