I am back to a calculus review problem today. I am just not sure where I want Math Mondays to finally settle. So for now I will just grab and solve whichever problem is at hand.

Here it is:

A merchants daily inventory over a 30 day period is given by

, where x is the number of days from 0 to 30, inclusive.

What is the merchant’s average daily inventory over the 30-day period?

So I am thinking I want to find the integral to get the total….but I have some questions about that. If I want daily, do I really want the area under the curve for the total inventory? To me it makes more sense to use Sigma….for the summation from 0 to 30. Regardless of how I find the sum, I will then divide by 30 to get the average.

So lazy student moment here. I really just want to find the inventory on day 0…(1200) and on day 30 (487.88) and then find the average. This is approximately $844.00. Which is a choice.

My not at lazy approach was to find the integral of the function and divide by 30.

To get approximately 791. Which is also a choice. And the choice I am making.

Long story short, I think I conceptually understand why I want the area. I am picturing 30 rectangles with a width of 1 and an average height of the function value f(0) and f(1), f(1) and f(2), etc. Finding the sum of these rectangles (or the total area under the curve to be more accurate) and dividing by 30 gives the average daily inventory.

Am I right?

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