Return to Assignments Area and volume
Assignment 3
Calculate the area which is enclosed by the lines 
and 
and the graph of the quadratic function 
. This assignment is relevant for the calculation of the Producer Surplus (see Bradley T. en Patton P., Essential Mathematics for Economics and Business, 2e ed., John Wiley, p. 418).
Solution
The intersection point of the graph of the quadratic function and the line is 
. Thus the area is equal to the area of the rectangle through the points 
and 
minus the area enclosed by the graph and the 
-axis, between and 
:
![\displaystyle40\cdot4-\int_{0}^{4}(Q^2+6Q)dQ=160-[\frac{1}{3}Q^3+3Q^2]_{0}^{4}=90.6667](https://4mules.nl/wp-content/ql-cache/quicklatex.com-1619041052a2359724e0b3e230c0f44f_l3.svg "Rendered by QuickLaTeX.com")
Return to Assignments Area and volume
