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

[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

 

[haruspex]

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.

 

[UnivMathProdigy]

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.

 

[haruspex]

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.

See https://en.m.wikipedia.org/wiki/Trigonometric_integral#Sine_integral