Given that the integral is given as [tex]\int_{0}^{12} f(t) dt[/tex], Hence, we are required to find the area under the graph where t is between 0 and 12. The correct answer is 2 (Option A) See the explanation below.
What is an integral?
An integral is a function of which a given function is the derivative, that is, when differentiated, it returns that function, and it can express the area under the curve of a graph of the function.
Hence the areas under the graph for the above function are given as:
12 + 6 + 2 + (-2) + (-16)
= 20-18
= 2
Notice that the following figures were arrived at by dividing the areas under the graph into common geometric shapes and deriving their area.
For example, the first three positive values were derived by dividing the positive part of the graph into two triangles and a rectangle.
The length of the rectangle is 6 while its height is 2
Area of a rectangle is L x W
= 6 * 2
= 12
It is to be noted that the areas under the curve are negative hence the negative results. See the attached image.
Learn more about graphs at:
https://brainly.com/question/19040584
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