Compute the area of the region S between the graph of f and g over the interval [0,2]
if f(x) = x(x-2) and g(x) = x/2
The Attempt at a Solution
The result is
a(S) = [tex]\int_0^2 [g(x) - f(x)] dx [/tex] = [tex]\int_0^2 (5x/2 - x^2) dx [/tex] = 5/2 2^2/2 - 2^3/3 = 7/3
This problem is in page 89 of apostol's vol 1 calculus.
I dont understad well where did [tex]\int_0^2 (5x/2 - x^2) dx [/tex] come from. Im starting to study integral calculus so this is relatively new to me. Could someone explain to me where did [tex]\int_0^2 (5x/2 - x^2) dx [/tex] come from?, and to explain the rest of the process.
I would appreciate it thanks in advance.