E^(t^2) i solved it, but can you verify please?

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SUMMARY

The discussion revolves around the verification of a solution to the integral of the function E^(t^2). Participants clarify that the user mistakenly derived both sides of the equation instead of correctly finding the integral. The fundamental theorem of calculus is referenced as a key concept in understanding the relationship between derivatives and integrals. The distinction between finding an integral and a derivative is emphasized as critical for solving the problem accurately.

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  • Understanding of the fundamental theorem of calculus
  • Knowledge of differentiation and integration techniques
  • Familiarity with exponential functions, specifically E^(t^2)
  • Basic algebraic manipulation skills
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  • Practice solving integrals involving exponential functions
  • Learn the differences between differentiation and integration
  • Explore examples of common mistakes in calculus to avoid errors
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Students studying calculus, educators teaching mathematical concepts, and anyone seeking to improve their understanding of integrals and derivatives.

seto6
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Homework Statement



so this is the problem:

2sbvds1.png


Homework Equations



The fundamental therom of calculus: http://mathworld.wolfram.com/FundamentalTheoremsofCalculus.html


The Attempt at a Solution



here is what i did, is this valid to do so. {sorry for being large}

as you can see i derived both sides to get that.:::::::
drfnmu.jpg
 
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It looks fine, except you aren't finding the integral. You are finding the DERIVATIVE of the integral. Try to be clear on that.
 

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