Step-by-step math courses covering Pre-Algebra through Calculus 3.
 

Master Multiple Integrals

Learn everything from Multiple Integrals, then test your knowledge with 230+ practice questions

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Multiple Integrals Testimonial

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“I have had the pleasure of being a student of Krista since Calculus I and she is consistently very thorough and very knowledgeable about her subject. Excellent preparation for anyone including/especially for a math major which I am.”
 
 
Multiple Integrals course summary

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Course Summary

Learn everything you need to know to get through Multiple Integrals and prepare you to go into Vectors with a solid understanding of what’s going on. Video explanations, text notes, and quiz questions that won’t affect your class grade help you “get it” in a way most textbooks never explain.

 
 
Multiple Integrals course outline

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Course outline

The curriculum includes:

  1. Approximating double integrals

    1. With rectangles

    2. Midpoint rule

    3. Riemann sums

  2. Double integrals

    1. Average value over the region

    2. Double integrals and iterated integrals

    3. Type I regions and type II regions (type 1 and type 2)

    4. Surface area

    5. Volume of the solid

    6. Changing the order of integration

  3. Double polar integrals

    1. Changing iterated integrals to polar coordinates

    2. Changing double integrals to polar coordinates

    3. Sketching area in polar coordinates

    4. Area in polar coordinates

    5. Volume in polar coordinates

  4. Applications of double integrals

    1. Mass and center of mass of the lamina

    2. Moments of inertia and radii of gyration

  5. Approximating triple integrals

    1. Midpoint rule

  6. Triple integrals

    1. Iterated triple integrals and triple integrals

    2. Average value over the region

    3. Volume of the solid

    4. Expressing the integral six ways

    5. Type I regions, type II regions, and type III regions (type 1, type 2 and type 3)

  1. Triple integrals in cylindrical coordinates

    1. Cylindrical coordinates

    2. Changing triple integrals to cylindrical coordinates

    3. Volume of the solid

  2. Triple integrals in spherical coordinates

    1. Spherical coordinates

    2. Changing triple integrals to spherical coordinates

    3. Volume of the solid

  3. Change of variables

    1. Jacobian of the transformation in two variables

    2. Jacobian of the transformation in three variables

    3. Evaluating double integrals

    4. Equations of the transformation

    5. Image of the set under the transformation

  4. Applications of triple integrals

    1. Mass and center of mass of the lamina

    2. Moments of inertia

 
 
Subscribe to the Multiple Integrals course

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Ready to Master Multiple Integrals?

 
Multiple Integrals course
 
 

By signing up for the Multiple Integrals course, you'll gain access to:

  • Step-by-step videos

  • Course notes and flashcards

  • Practice quizzes

  • Bonus practice workbooks

  • Comprehensive formula sheets

  • Summary study sheets

  • Practice final exams

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