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

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The discussion revolves around a calculus problem involving the function E^(t^2). The original poster attempts to solve the problem by deriving both sides of the equation but is corrected for not actually finding the integral. Participants emphasize the importance of distinguishing between finding an integral and its derivative. Clarity in mathematical communication is highlighted as essential for solving such problems. The thread underscores the need for accurate terminology in calculus discussions.
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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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