The demand function

where

*p* = price in dollars and

*x* = sales level in hundreds, is pictured below.

The area of the grey rectangle in the picture has area = sales level times price = revenue generated by sales.

The area of the shaded portion under the curve above the rectangle represents the consumers' surplus.

for a sales level of 900 ...

First find the price

... evaluate p(900)
then revenue from sales

... 900[p(900)]
consumers' surplus

... $\displaystyle \textcolor{red}{\int_0^{900} p(x) \, dx}$

- 900[p(900)]
Note: The consumers' surplus formula involves

*p(x)* and hence

*x* values must be in hundreds. The output of the consumers' surplus integral is in hundreds of dollars though, so be careful with your units!