Definite Integration with Upper bound as another integral.

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SUMMARY

The discussion centers on the challenges faced in solving a definite integral where the upper bound is another integral, highlighting the confusion between two methods of differentiation. The first method, which involves finding the general form before evaluating, is confirmed as correct. In contrast, the second method, which incorrectly applies direct substitution before differentiation, leads to erroneous results. This emphasizes the importance of the correct order of operations in calculus, particularly in dealing with non-elementary functions.

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  • Study the Fundamental Theorem of Calculus
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Hi guys, just got owned by my calc prof with a final exam question. Very very weird. Attempted it and different approach apparently gets u different answers. I have no idea what's going on..

View attachment Exam question.doc
I have attached the question as a word document. Too much integration to type and I cannot really use the Latex Reference well. Equation Builder in Microsoft Word is more helpful for me.

I have noticed too that the upper bound integral forms a non-elementary function thus I am unsure if my methods are right. The prof obviously wants us to really think hard. I sure hope the 1st approach of finding the general form first is right. The 2nd method of direct substitution from the initial start seems weird.

Thanks everyone for your help!
 
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Your first method is correct. Your second method fails because you are essentially claiming that G'(0)=\frac{d}{dy}G(0), which is nonsense. You must first differentiate and then plug in the point at which you want to find the derivative; doing things the other way around will always give you zero, regardless of the function you are differentiating.
 
YAY! THANKS! :D:D:D now i have ease of mind about my exam! :D:D:D thanks!

yeah i realized that too which doesn't seem to be making sense. the prof is one hell of a tricky guy. he loves doing stuff like that.

Thanks!
 

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