Graph both functions in your calculator or on graph paper to see
what
the
area looks like.
The area between the functions can be found by summing
rectangular
areas
whose heights are given by the upper function minus the lower function,
in this case, -x(x - 4) - x. The widths of the
rectangles
are Dx.
Find the intersection of the two functions to find the limits of
integration.
x = - x(x - 4) x = - x2 + 4x 0 = - x2 + 3x 0 = -x (x - 3) x = 0, 3