Solve for Integral of Tricky Function in Calculus | Math Subject GRE

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    Function Integral
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Discussion Overview

The discussion revolves around evaluating the indefinite integral of the function \(\int \frac{\sin t}{t} \, dt\) and its relation to finding the local maximum of a function defined by this integral. The context includes calculus concepts relevant to the math subject GRE, particularly focusing on the application of Leibniz's rule.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires about the possibility of evaluating the integral \(\int \frac{\sin t}{t} \, dt\).
  • Another participant suggests that solving the integral may not be necessary to determine the local maximum of the function \(f(x) = \int_{x}^{2x} \frac{\sin t}{t} \, dt\).
  • A participant acknowledges that the integral does not need to be solved for the local maximum question but still expresses interest in the general evaluation of the integral.
  • A later reply references a Wikipedia page on the sine integral, indicating that there may be existing information on the topic.

Areas of Agreement / Disagreement

Participants generally agree that the integral does not need to be evaluated to find the local maximum, but there is no consensus on whether the integral itself can be evaluated.

Contextual Notes

The discussion does not clarify the specific methods or conditions under which the integral might be evaluated, nor does it address any assumptions related to the integral's convergence or definitions.

UnivMathProdigy
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Hi, everyone.

I was working on a calculus question related to the math subject GRE and I was wondering if it's possible to evaulate this indefinite integral:

\int {\frac{\sin t}{t}} \, dt

The actual question involves Leibniz's rule of differentiating integrals and didn't think of it at the time I worked on it. The main gist of it was finding the local maximum on the interval (0,\frac{3\pi}{2}) of the following function:

f(x) = \int_{x}^{2x} \frac{sin t}{t} \ dt
 
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It's not clear from your post whether you realize it is quite unnecessary to solve the integral in order to answer that local max question.
 
I do realize that I didn't need to solve the integral to find the local max. I was just wondering if the general integral stated first is possible to evaluate.
 

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