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

1-4.

Examine the graph the function $f(x) = 5 - x$ at right.

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

Notice the familiar geometric shape.

 We will use the notation $A(f, 0 ≤ x ≤ 5)$ to represent "The area between the function and the $x$-axis" over the interval from $x = 0$ to $x=5$.
1. Notice that the line dips below the $x$-axis when $x > 5$. We will consider the area below the $x$ -axis as negative. Find $A(f, 0 ≤ x ≤ 7)$.

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

$A (f, 0 ≤ x ≤ 5) + A (f, 5 ≤ x ≤7)$

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

$A (f, 0 ≤ x ≤ 5) + A (f, 5 ≤ x ≤ k)$

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