Consider the following for the two (02) items that follow: Let the curve f(x) = |x - 3| . What is the area bounded by the curve f(x) and y = 3 ?

Step-by-step solution

The given curve is y = |x - 3| and the line is y = 3 . To find the points of intersection, we equate the two equations: |x - 3| = 3 x - 3 = 3 or x - 3 = -3 x = 6 or x = 0 The points of intersection are (0, 3) and (6, 3) . The vertex of the curve y = |x - 3| is at (3, 0) . The area bounded by the curve and the line forms a triangle with vertices (0, 3) , (6, 3) , and (3, 0) . The length of the base of this triangle (along the line y = 3 ) is 6 - 0 = 6 units. The height of the triangle (perpendicular distance from th