D.E. + Integration: Find Value of k

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Homework Help Overview

The discussion revolves around a differential equation and integration problem, specifically focusing on finding a value of k based on given functions and integrals. The context includes the application of the Fundamental Theorem of Calculus.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the necessity of integrating the first function to determine f(x) and question its integrability. There are suggestions to rewrite the second integral and make substitutions to facilitate the integration process.

Discussion Status

The discussion is active with various approaches being proposed, including integration techniques and substitutions. Some participants express uncertainty about the relevance of the initial statement, while others clarify its importance in the context of the problem.

Contextual Notes

There are indications of confusion regarding the integration of the first function and its role in the overall problem. Participants are navigating through assumptions about the functions involved and their integrability.

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Homework Statement



Let [URL]http://203.196.176.41/VLEBT_RootRepository/Resources/b38e1b90-9ba0-45c6-a1eb-65288fa31b27.gif,[/URL] x > 0. If [URL]http://203.196.176.41/VLEBT_RootRepository/Resources/47280b1e-999e-44b0-a05e-5ad5243b0750.gif,[/URL] then one of the possible values of k is

1)16
2)63
3)64
4)15

The Attempt at a Solution



Do I have to integrate the first function to find out f(x)? I think that function is non-integrable.
 
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If you write the 2nd integral as: [tex]\int ^4 _1 \frac {3e^{sint^3}} {t} dt[/tex] and then let x = t3, you will see the way :wink:
 
I got it. But then there is no use of the first sentence, right?
 
"Fundamental Theorem of Calculus"! That first part is telling you that, in the second part, you are integrating the derivative of f.
 
@Abdul Quadeer: Not sure what you meant :rolleyes:
 
Once you make the substitution u= x^3 as hikaru1221 suggested, you will be integrating (df/du)du. What is that integral?
 

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