#### To determine

**To evaluate:**

The integral ∫0913x-2dx by interpreting it in terms of area.

#### Answer

-92

#### Explanation

**1) Concept:**

A definite integral can be interpreted as a net area, that is, as a difference of areas;

∫abf(x)dx=A1-A2

where A1 is the region above x- axis and below the graph of f, and A2 is the region below x- axis and above the graph of f

**2) Formula:**

Area of a triangle : A=12bh

where b is the base and h is the height

**3) Given:**

∫0913x-2dx

**4) Calculation:**

∫0913x-2dx can be interpreted as the area under the graph of

fx= 13x-2 between x= 0 and x=9

The graph of y=13x-2 is the line with the slope 13 as shown in the figure below,

Now, find the integral as the difference of the areas of the two triangles by using the graph.

A1 is the region above x- axis and below the graph of f.

By using the formula of the area of a triangle,

A1=12*3*1=32

A2 is the region below x-axis and above the graph of f.

By using the formula of the area of a triangle,

A2=12*6*2=6

Therefore by using the concept,

∫0913x-2dx=A1-A2=32-6 =-92

**Conclusion:**

∫0913x-2dx=A1-A2=-92