Practice Practical Applications - 4.6 | 4. Numerical Integration | Mathematics - iii (Differential Calculus) - Vol 4
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

Practical Applications

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.

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the main purpose of numerical integration?

💡 Hint: Think about scenarios where exact answers are hard to find.

Question 2 Easy

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

Question 1

What is the main application of numerical integration?

To solve differential equations
To approximate definite integrals
To find exact solutions

💡 Hint: Consider what numerical methods are designed for.

Question 2

True or False: Simpson's Rule can be used only if the number of intervals is odd.

True
False

💡 Hint: Think about the requirements for applying Simpson's Rule.

Get performance evaluation

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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.