# Area under the curve for Exponential function

#### y_shalaby

I am currently doing an economics dissertation and I need help with the following question:
Consider a subset of an exponential function with upper bound a and lower bound b. I divide the area under the curve in this section into Q sub-areas P such that the distance between subsequent divisions is equal.
I need an equation that takes the sum of squares of the resulting areas.
I would really appreciate some guidance!

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#### skipjack

Forum Staff
I need an equation that takes the sum of squares of the resulting areas.
Why does that have any connection with economics?

Start by inventing an equation for the exponential function. Do you know how to integrate it?

#### y_shalaby

Why does that have any connection with economics?

Start by inventing an equation for the exponential function. Do you know how to integrate it?
I need to calculate the Herfindahl index of an industry (which is calculated by taking the sum of squares of each firm's share of total employment). I am assuming in my thesis that the employment shares of firms are exponentially distributed. However, the data I am given only specifies the sizes of firms using intervals and I am given the number of firms in each interval.

Yes I know how to integrate.
Thank you!

#### skipjack

Forum Staff
You may have to estimate each firm's share, but you'll still need to decide on the exponential function, so that you can integrate it.

#### y_shalaby

You may have to estimate each firm's share, but you'll still need to decide on the exponential function, so that you can integrate it.
Yes, I already estimated a function using maximum likelihood estimation.