Double Integral of sin(x^2) on TI-89

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    Integral Ti-89
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Homework Help Overview

The discussion revolves around evaluating a double integral of the function sin(x^2) over a specified range. The original poster expresses difficulty in computing the integral using a TI-89 calculator and notes that the function does not appear in integral tables.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the lack of an elementary anti-derivative for sin(x^2) and question whether the original poster intended to compute the double integral in a specific order. There is mention of the possibility of reversing the order of integration to facilitate computation.

Discussion Status

The conversation is ongoing, with participants exploring different interpretations of the problem and suggesting alternative approaches, such as reversing the order of integration. There is no explicit consensus yet on how to proceed with the calculations.

Contextual Notes

Participants note that the second part of the problem requires finding a corresponding double integral in a different order that yields the same value, indicating a potential constraint in the problem setup.

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Homework Statement


[tex]\int\stackrel{9}{0}\int\stackrel{9}{y}sin(x^2)dxdy[/tex]

Homework Equations





The Attempt at a Solution


I don't see where there's enough "stuff" to play with to get past the first integration. My TI-89 can't do it and sin(x2) isn't in my integrals tables.

Sorry about the LATEX issues. It's correctly presented now. I'm looking at my assignment and I'm 100% sure this is what the professor asked for.
 
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I can't really decipher your LaTex code, but ∫sin(x2) dx has no elementary anti-derivative.

so normally you can't compute it

[tex]\int \int sin(x^2) dxdy[/tex]

One can't find this

though one can find

[tex]\int \int sin(x^2) dydx[/tex]

Were you trying to compute a double integral by chance?
 
What you can do is reverse the integral, since dxdy = DA.

So swap the integral and find the volume with respect to dydx
 
The second part of the problem asks for a corresponding dydx double integral (and associated integration ranges) that would give you the same value once computed.
 

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