Graph f(x)=x(x+4)(3−x). Then, using a calculator, find the total area between the graph and the x-axis between x=−4 and x=3.
area =
Next, find
∫^{3}_−4f(x)dx=
Interpret the value of the integral in terms of areas. Be sure you can indicate how it is related to the answer you got for the total area between the graph and the x-axis between x=−4 and x=3.
for the geometric area, you want
∫[-4,3] |x(x+4)(3-x)| dx = 937/12
But
∫[-4,3] x(x+4)(3-x) dx = -343/12
because the larger portion of the area lies below the x-axis, and is algebraically negative