### Home > APCALC > Chapter 1 > Lesson 1.1.1 > Problem 1-4

1-4.

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 ≤ *x* ≤ *k* is 0. Show how you obtained your answer clearly and completely.

*A* (*f*, 0 ≤ *x* ≤ 5) + *A* (*f*, 5 ≤ *x* ≤ *k*)