AUC40 An investment in a certain mining operation is returning an amount per month that follows the following formula

where x is the month and A is the amount for that month.  This formula is valid for 40 months.

What is the total return for the first 12 months?

Solution: The curve starts out at $300 for the zero^th month and drops off with time. In this problem the height of a rectangle under the curve for each value of x represents the money received that month and the sum of these rectangles is the total amount for the period summed. For 12 months this sum is the area under the curve from the zero^th to the eleven^th month, or the integral from 0 to 11.