Interpret Riemann sum to determine integral

[stunner5000pt]

Homework Statement

What is the integral representation of the following limit

$$lim_{n \rightarrow \inf} \frac{\pi}{2n} \Sigma_{i=1}^{n} \ln ( \frac{pi}{4} + ( \frac{i \pi}{2n} )^2)$$

Relevant Equations

Riemann sums & integrals formula

Just looking at the summand, I can see that the function is

ln(pi/4 + x^2)

as the (i pi/2n) term is the 'x' term.

How do I determine the limits of the integral, however? I was thinking about using the lower bound of the summation --> this given the (pi / 2n)^2 term, implying that nothing was 'added' as the 'left' side bound. So I conclude that the lower limit, which we'll call a = 0

And then using the pi / 2n = (b - a)/n where a and b are the lower and upper bounds respectively, we can solve for the upper bound b.

Is this reasoning correct? Let me know if there is something that I might've missed to consider ?

Thank you in advance

 

[FactChecker]

Good work. The summation goes from $i=1$ to $i=n$. What does that mean for the values of $x$?

 

[stunner5000pt]

Good work. The summation goes from $i=1$ to $i=n$. What does that mean for the values of $x$?

I see it now - testing the upper bound of the summand in the 'x' term gives pi/2

Thanks very much for your help!