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

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• UnivMathProdigy
In summary, the conversation discusses a calculus question related to the math subject GRE, specifically an indefinite integral involving the function f(x) = \int_{x}^{2x} \frac{sin t}{t} \ dt. The speaker initially asked if it was possible to evaluate the integral, but another participant points out that it is unnecessary for finding the local maximum on the given interval. The conversation also references Leibniz's rule of differentiating integrals and provides a Wikipedia link for further information.

#### UnivMathProdigy

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:

$f(x) = \int_{x}^{2x} \frac{sin t}{t} \ dt$

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.

## 1. What is the definition of an integral?

The integral is a mathematical concept used to determine the area under a curve or the accumulation of a quantity over an interval. It is denoted by the symbol ∫ and is the inverse operation of differentiation.

## 2. What is a tricky function?

A tricky function is a mathematical function that is difficult to integrate using traditional methods. This can include functions with complex or nested expressions, non-elementary functions, or functions with no closed-form solution.

## 3. How do you solve the integral of a tricky function?

Solving the integral of a tricky function often involves using advanced techniques such as integration by parts, substitution, or partial fractions. In some cases, it may also be necessary to use numerical methods or computer software to approximate the solution.

## 4. Can all tricky functions be integrated?

No, not all tricky functions have a closed-form solution. Some functions, such as the Gaussian integral, do not have an elementary antiderivative and must be approximated using numerical methods.

## 5. How is the integral of a tricky function used in science?

The integral of a tricky function is an important tool in many scientific fields, including physics, engineering, and economics. It allows for the calculation of quantities such as work, displacement, and revenue, which are essential for understanding and predicting real-world phenomena.

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