Definite Integration with Upper bound as another integral.

In summary, the speaker had a difficult final exam question in calculus and tried different approaches, but was unsure if their methods were correct due to the non-elementary function and the professor's challenging style. They received help from others and discovered that their first method was correct, but their second method failed due to an incorrect assumption. They express relief and gratitude for the assistance and comment on the professor's tricky nature.
  • #1
xxviatorxx
2
0
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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  • #2
Your first method is correct. Your second method fails because you are essentially claiming that [itex]G'(0)=\frac{d}{dy}G(0)[/itex], 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.
 
  • #3
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!
 

FAQ: Definite Integration with Upper bound as another integral.

1. What is definite integration with upper bound as another integral?

Definite integration with upper bound as another integral is a mathematical concept in which the upper bound of an integral is itself an integral. This means that the value of the upper bound is determined by the integration of a function.

2. How is definite integration with upper bound as another integral useful?

This concept is useful in solving complex integrals that involve nested or multiple integrals. It allows us to simplify the integration process and find the solution using well-known integral formulas.

3. Can you provide an example of definite integration with upper bound as another integral?

Sure, an example of this concept is the double integral of a function f(x,y) with upper bound g(x). This can be written as ∫∫f(x,y) dxdy, where the upper bound of y is determined by the integration of function g(x).

4. What is the difference between definite integration with upper bound as another integral and regular definite integration?

The main difference is that in regular definite integration, the upper bound is a constant value, while in definite integration with upper bound as another integral, the upper bound is a function that is integrated.

5. Are there any specific rules or techniques for solving definite integration with upper bound as another integral?

Yes, there are specific rules and techniques for solving these types of integrals, such as the substitution method and integration by parts. It is also important to carefully consider the limits of integration when setting up the integral.

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