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Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and find the area using geometry. [0,1] |9x-3|

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Answer:

2.5

Step-by-step explanation:

The integral of a function is the area under the curve.

Graph |9x−3|.  The result is two lines.  The areas under these lines are triangles.  The first triangle has a base of ⅓, and a height of 3.  The second triangle has a base of ⅔, and a height of 6.

The total area is therefore:

A = ½ (⅓) (3) + ½ (⅔) (6)

A = ½ + 2

A = 2.5

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