# What is the net area between #f(x) = 2x-6 # and the x-axis over #x in [2, 4 ]#?

##### 1 Answer

2 units squared.

#### Explanation:

You can go about this in two ways: Algebra and Integrals.

**Algebra**

y = 2x-6 is linear, thus if we take the value over the x interval [2,4] we can use geometry to calculate the area.

graph{2x-6 [-2.27, 7.73, -2.18, 2.82]}

You can see two triangles in the graph (you could also find this algebraically). Thus, you can calculate the area.

**Integrals**

An integral gives the area under the curve. Remember though that *if a function goes below the X axis, the integral is negative* Thus you have to do two separate integrals based on the X intercept.

*finding the X intercept (that is where y = 0)*

When *negative integral from 2 to 3* and the *positive integral from 3 to 4*