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

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    Function Integral
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SUMMARY

The discussion centers on evaluating the indefinite integral of the function \(\int \frac{\sin t}{t} \, dt\), which is known as the Sine Integral. The user also explores finding the local maximum of the function \(f(x) = \int_{x}^{2x} \frac{\sin t}{t} \, dt\) on the interval \((0, \frac{3\pi}{2})\). It is concluded that solving the integral is unnecessary for determining the local maximum, highlighting the application of Leibniz's rule for differentiating integrals in this context.

PREREQUISITES
  • Understanding of calculus concepts, specifically integrals and differentiation.
  • Familiarity with Leibniz's rule for differentiating under the integral sign.
  • Knowledge of the Sine Integral function and its properties.
  • Basic skills in evaluating local maxima of functions.
NEXT STEPS
  • Research the properties and applications of the Sine Integral function.
  • Study Leibniz's rule in detail, focusing on its use in calculus problems.
  • Explore techniques for finding local maxima and minima of functions.
  • Practice evaluating definite and indefinite integrals involving trigonometric functions.
USEFUL FOR

Students preparing for the Math Subject GRE, educators teaching calculus, and anyone interested in advanced integral calculus techniques.

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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