Refer to the Information in the Graph Below $x ^ { 2 }$

question 40

Multiple Choice

Refer to the information in the graph below. Given functions f(x) = $x ^ { 2 }$ + 4x + 4 and g(x) = $x ^ { 2 }$ - 4x + 4, set up a definite integral or sum of definite integrals that gives the area of the shaded portion.

• A) \(\int _ { - 2 } ^ { 0 } - 8 x d x + \int _ { 0 } ^ { 2 } 8 x d x\)
• B) \(\int _ { - 2 } ^ { - 4 } \left[ \left( x ^ { 2 } - 4 x + 4 \right) - \left( x ^ { 2 } + 4 x + 4 \right) \right] d x\)
• C) \(\int _ { - 2 } ^ { 0 } 8 x d x\) + \(\int _ { 0 } ^ { 2 } - 8 x d x\)
• D) \(\int _ { - 2 } ^ { 2 } \left[ \left( x ^ { 2 } - 4 x + 4 \right) - \left( x ^ { 2 } + 4 x + 4 \right) \right] d x\)
• E) none of these

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Definitions:

Z Distribution

A normal distribution with a mean of zero and a standard deviation of one, also known as a standard normal distribution.

95th Percentile

A value below which 95% of the data points in a data set fall.

Mean

The arithmetic average of a set of values or quantities, calculated by dividing the total of all values by the number of values.

Standard Normal

A normal distribution with a mean of zero and a standard deviation of one, used as a basis for comparison with other normal distributions.