How to change the order of a triple integral | Summary and Q&A

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April 8, 2018
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blackpenredpen
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How to change the order of a triple integral

TL;DR

This video demonstrates how to change the order of integration in a triple integral and provides a step-by-step guide.

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Questions & Answers

Q: Why is it important to be able to visualize the solid being integrated in a triple integral?

Visualizing the solid helps in determining the limits of integration for each variable and understanding how the integrand will change with different orders of integration. It allows for a better understanding of the integral as a whole.

Q: How many ways are there to organize the differentials dy, dx, and dz in a triple integral?

There are a total of six ways to organize the differentials dy, dx, and dz. This is because for three differentials, there can be three factorial possible arrangements, which is equal to six.

Q: How can the 3D representation of the shape be drawn for visualization?

The presenter suggests starting with the x-axis, then the positive y-axis, and finally the z-axis to draw the 3D picture. The shape can be represented by drawing the different planes and curves corresponding to the variables being integrated.

Q: How do you determine the limits of integration for each variable when changing the order of integration?

By analyzing the equations and functions involved, the limits of integration can be determined. The video demonstrates the step-by-step process of determining the limits for each variable using the given example.

Summary & Key Takeaways

  • The video explains the process of changing the order of integration in a triple integral, specifically from dz dy dx to dx dy dz.

  • The presenter emphasizes the importance of visualizing the solid being integrated and provides a method for drawing a 3D representation of the shape.

  • The video shows how to determine the limits for each variable and construct the integrand based on the new order of integration.

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