# Math Help - economics with integral

1. ## economics with integral

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 - x2. Hence, a quantity of 4 units of the good will be bought at a price of $9, i.e. for a total payment of$36. However, the total amount the consumer was willing to pay is given by the area between the graph of y =30 - x2 and the x-axis from x = 0 to x = 4. Find this value. How much does it differ from the actual payment of $36? This difference is known as ‘consumer surplus’. 2. Hello, Translating the text, the total price the consumer is willing to pay for 4 units is : $\int_0^4 y ~dx=\int_0^4 (30-x^2) ~dx=\left[30x-\frac{x^3}{3}\right]_0^4=\dots$ Compare it to 36$ and that's all