- #1
Reversing Order of Integration: Double Integral Evaluation
- Thread starter BrownianMan
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- Double integral Integral
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Homework Help Overview
The discussion revolves around evaluating a double integral by reversing the order of integration, focusing on the setup and interpretation of the integration limits based on a defined region.
Discussion Character
- Exploratory, Problem interpretation
Approaches and Questions Raised
- Participants discuss the importance of sketching the region of integration to understand the limits for both the inner and outer integrals. There is mention of specific functions that define the boundaries of integration.
Discussion Status
Some participants have provided guidance on visualizing the problem through sketching, while others express uncertainty about the next steps in the evaluation process. Multiple interpretations of the integral setup are being explored.
Contextual Notes
Participants note specific ranges for the variables involved, such as x ranging from cuberoot(y) to 2 and y ranging from 0 to 8, which are critical for understanding the integration limits.
![gif.latex?\int_{0}^{8}\int_{\sqrt[3]{y}}^{{2}}7e^{x^4}dxdy.gif](/data/attachments/121/121114-9c5994283ab8624f2d7259db665996dc.jpg?hash=nFmUKDq4Yk){kind=small}
- #2
Mark44
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The first step in this type of problem is to sketch a graph of the region over which integration is taking place. For the inner integral, x ranges from cuberoot(y) to 2. For the outer integral, y ranges from 0 to 8. Sketch the graphs of x = y1/3 and x = 2, and then sketch the graphs of y = 0 and y = 8. For the iterated integral with the opposite order, the inner integration limits will involve two functions of y, and the outer integration limits will involve two x values.BrownianMan said:Evaluate the integral by reversing the order of integration.
![gif.latex?\int_{0}^{8}\int_{\sqrt[3]{y}}^{{2}}7e^{x^4}dxdy.gif](https://www.physicsforums.com/attachments/gif-latex-int_-0-8-int_-sqrt-3-y-2-7e-x-4-dxdy-gif.138033/ "gif.latex?\int_{0}^{8}\int_{\sqrt[3]{y}}^{{2}}7e^{x^4}dxdy.gif")
I'm not exactly sure how to approach this problem. Any help would be appreciated!
- #3
BrownianMan
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Ok, so would the answer be
- #4
Mark44
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Yep.
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