Question

Let A(x) represent the area bounded by the graph, the horizontal axis, and the vertical lines at and t = x for the graph below. Evaluate A(x) for x = 1,2,3, and 4

Answer 1

• A(1)=4

,

• A(2)=8

,

• A(3)=13

,

• A(4)=17.5

Explanation:

The graph is given below:

The area, A(x) represents the area bounded by the graph, the horizontal axis, and the vertical lines at t=0 and t = x.

(a)A(1)

Area, A(1) is the area of a trapezoid in which: a=3, b=5 and h=1

`\begin{gathered} \text{ Area of a trapezoid}=(1)/(2)(a+b)h \\ A(1)=(1)/(2)(3+5)(1)=(1)/(2)*8=4\text{ square units} \end{gathered}`

(b)A(2)

.

`A(2)=2* A(1)=2*4=8\text{ square units}`

(c)A(3)

.

`\begin{gathered} A(3)=A(2)+(5*1) \\ =8+5 \\ =13\text{ square units} \end{gathered}`

(d)A(4)

`\begin{gathered} A(4)=A(3)+\text{ Area of shape 4} \\ =13+(1)/(2)(5+4)(1) \\ =13+(9)/(2) \\ =13+4.5 \\ =17.5\text{ square units} \end{gathered}`