### Home > PC > Chapter 8 > Lesson 8.1.1 > Problem8-11

8-11.

Given the piecewise function $h ( t ) = \left\{ \begin{array} { l l l } { 4 } & { \text { for } } & { 0 \leq t \leq 4 } \\ { t } & { \text { for } } & { 4 < t < 6 } \\ { 6 } & { \text { for } 6 \leq t \leq 10 } \end{array} \right.$, complete the following problems.

1. Graph $h\left(t\right)$ over the interval $0 ≤ t ≤ 10$.

2. What is the area under $h\left(t\right)$ over the interval $≤ t ≤ 10$?

Break the area into smaller rectangles and triangles. Calculate the area for each. Add up the areas of the parts.

3. If $g\left(t\right) = h\left(t\right) + 6$, what is the area under $g\left(t\right)$ for the same interval?

Raising the graph up $6$ would give the area an additional $\left(6\right)\left(\text{width}\right)$.