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The shaded area between the x and y axes and the line y=-x+5 Examine the graph the function f (x) = 5 – x at right. Homework Help ✎

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 ≤ xk is 0. Show how you obtained your answer clearly and completely.

A (f, 0 ≤ x ≤ 5) + A (f, 5 ≤ xk)