Definite Integration with Upper bound as another integral.

[xxviatorxx]

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!

 

[gabbagabbahey]

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.

 

[xxviatorxx]

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!