Find the area enclosed by the curve y = 3x - x^2 and the x-axis

Start with finding limits by setting 3x - x^2 = 0, then factorise x(3 - x) = 0. Therefore x = 0 or 3. The area is the integral of 3x - x^2 between x = 0 and 3, sub in 3 and 0 into 3(x^2)/2 - (x^3)/3, which gives 3*(3^2)/2 - (3^3)/3 - 0 = 9/2 square units.