### Home > CALC > Chapter 1 > Lesson 1.1.1 > Problem1-4

1-4.
1. Examine the graph the function f(x) = 5 − x at right. Homework Help ✎

1. Find the area of the shaded region using geometry.

2. Notice that the line dips below the x-axis when x > 5. We will consider the area below the x -axis as negative. Find A(f, 0 ≤ x ≤ 7).

3. Find k if A(f, 0 ≤ xk) = 0. Show how you obtained your solution clearly and completely.

Notice the familiar geometric shape.

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)

A (f, 0 ≤ x ≤ 5) + A (f, 5 ≤ xk)

$[\text{area from part a}]+\frac{1}{2}(k-5)(-k+5)=\underline{ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$