# Sketch the region whose area is represented by the definite integral. Integral from -2 to 8 of...

## Question:

Sketch the region whose area is represented by the definite integral.

{eq}\int_{-2}^{8} \left | x-4 \right | \, \mathrm{d}x {/eq}

Use a geometric formula to evaluate the integral.

## Area:

Recall that the area under a positive curve {eq}y=f(x),\, a\leq x\leq b {/eq} is given by the definite integral {eq}\int_a^b f(x)\, dx {/eq}. This was our original motivation for defining the integral and it allows us to evaluate the area under curves without standard geometric formulas.

## Answer and Explanation:

The region whose area is given by the integral {eq}\int_{-2}^8 \left| x-4\right| \, dx {/eq} is shown below

We also recall that the area of a...

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from Saxon Math 7/6 Homeschool: Online Textbook Help

Chapter 27 / Lesson 3