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What is J|X-2|dx (from 0 to 4). Drawing a picture of the V-shaped graph which touches

the x-axis at 2 helps. Geometry, not calculus.
a. O b. 1. c. 2 d. 4



I am having trouble trying to solve this problem can anyone help?

User GgDeGreat
by
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1 Answer

5 votes

Answer:

d. 4

Explanation:

We want to evaluate


\int _(0) ^(4) |x - 2| dx

geometrically.

The graph of


y = |x - 2|

is a V-shaped graph with vertex at (2,0).

Geometrically, we want to find the area under this curve from x=0 to x=4.

This V-shaped graph formed two congruent triangles as shown in attachment.

The area of the triangle with height 2 units and base 2 units is


= (1)/(2) bh


= (1)/(2) * 2 * 2


= 2 \: square \: units

Since the triangles are two we multiply by 2 to get:


= 4 \: square \: units

What is J|X-2|dx (from 0 to 4). Drawing a picture of the V-shaped graph which touches-example-1
User SamBrick
by
8.2k points

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