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100 Points
Use geometry to evaluate the integral from negative 2 to 6 of f of x, dx where f of x equals the absolute value of x for x between negative 2 and 2 inclusive, equals 2 for x greater than 2 and less than or equal to 4, and equals negative x plus 4 for x greater than 4 and less than or equal to 6.

100 Points Use geometry to evaluate the integral from negative 2 to 6 of f of x dx where f of x equals the absolute value of x for x between negative 2 and 2 in class=

Respuesta :

Answer:

[tex]\int\limits^{6}_{-2} {f(x)} \, dx=6[/tex]

Step-by-step explanation:

Review the attached graph

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Lanuel

By using geometry to evaluate the given integral, the value is equal to 6 units.

How to use geometry to evaluate an integral?

In order to use a geometry to evaluate a definite integral, you should identify the portion of a graph which corresponds to the given integral.

Also, you'll mark out the geometric shapes that are formed on the graph, so as to enable you calculate their areas. Finally, you'll add the areas together.

From the graph of the integral shown in the image attached below, the geometric shapes that are formed are rectangle and triangles.

For the area of rectangle, we have:

Area of rectangle = L × B

Area of rectangle = 2 × 2

Area of rectangle = 4 units.

For the area of triangle, we have:

Area of triangle = 1/2 × b × h

Area of triangle = 1/2 × 2 × 2

Area of triangle = 2 units.

Total area = 4 + 2

Total area = 6 units.

Read more on integrals here: https://brainly.com/question/5898524

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