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Examine the graph the function at right.

Calculate the area of the shaded region.

Notice the familiar geometric shape.

Notice that the line dips below the -axis when . When you are asked to calculate the “area under a curve” this refers to the region between the curve and the ‑axis. Any area below the -axis is considered to be negative. Calculate the area under the curve for .

Find the area of the negative region and combine
it with the positive area found in part (a).

Determine the value of k such that the area under the curve for is . Show how you obtained your answer clearly and completely.

Decreasing line passing through the points (0, comma 5), & (5, comma 0), with triangular area below the line, above the x axis, & right of y axis, shaded.