Let y be the price per unit of a good. The price a consumer is willing to pay for different quantities (x) of the good is given by the relation y = 30 - x^2. So a quantity of 4 units of the good will be bought at a price of $14, i.e. for a total payment of $56. However, the total amount the consumer was willing to pay is given by the area between the graph of y = 30 - x^2 and the x-axis from x = 0 to x = 4. Find this value. How much larger is it than the actual payment of $56? What is this difference called in economics?
I've got the x intercepts - and +squareroot30
and the y intercept 30
so it's an upside down parabola but not sure where to go from here.