Calculate the area of the shaded region.
Notice the familiar geometric shape.
Notice that the line dips below the x-axis when x > 5. When you are asked to calculate the “area under a curve” this refers to the region between the curve and the x‑axis. Any area below the x-axis is considered to be negative. Calculate the area under the curve for 0 ≤ x ≤ 7.
Find the area of the negative region and combine
it with the positive area found in part (a).
A (f, 0 ≤ x ≤ 5) + A (f, 5 ≤ x ≤7)
Determine the value of k such that the area under the curve for 0 ≤ x ≤ k is 0. Show how you obtained your answer clearly and completely.
A (f, 0 ≤ x ≤ 5) + A (f, 5 ≤ x ≤ k)