The graphs of two functions fx x2 4x and gx 1 x 12 are

The graphs of two functions f(x) = x2 - 4x and g(x) = 1 - (x - 1)2 are shown in the diagram. Find the boundaries of integration and evaluate the area between the two curves.

Solution

the area can be found by integrating g(x) - f(x) b/w x=0 and x = 3

g(x) - f(x) = -2x² + 6x = h(x) ....(let)

integrating this h(x) b/w x=0 and x=3 you will get result 9 which is the required area