## Lecture 16: Double integrals

Lecture 16: Double integrals
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Taught by OCW
Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 21, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.
Learn how to compute double integrals and what they are used for in Calculus.
• What is a double integral?
• How do you find a double integral?
• What does it mean geometrically to find a double integral?
• How do you find the volume below a multivariable function?
• How do you know which order to write dx and dy in double integrals?
• What is an iterated integral?
• How do you set up a double integral?
• What is the double integral of 1 - x^2 - y^2 dydx from 0 to 1 for x and y?
• How do you find the double integral of 1 - x^2 - y^2 dydx over the quarter disc region bounded by x^2 + y^2 = 1 in the first quadrant?
• How do you find the double integral of e^y/y dydx?
• How do you switch a double integral from dydx to dxdy?
This lesson is an introduction to double integrals of multivariable functions over regions in the plane. The professor explains very clearly the concept of what taking a double integral means, how to set up a double integral, and how to actually compute it. Some actual example problems are shown as well. This is a really good lesson on this topic. Some very difficult and confusing topics are covered.
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Reviewed by MathVids Staff on March 21, 2009.