Let $a$ And $b$ Be Real Numbers A) $\int _ { - \infty } ^ { 2 } \frac { 9 } { x ^ { 2 } + 10 } d x$

question 66

Multiple Choice

Let $a$ and $b$ be real numbers. What integral must appear in place of the question mark "?" to make the following statement true?
$$\int _ { - \infty } ^ { a } \frac { 10 } { x ^ { 2 } + 9 } d x + \int _ { a } ^ { \infty } \frac { 10 } { x ^ { 2 } + 9 } d x = ? + \int _ { b } ^ { \infty } \frac { 10 } { x ^ { 2 } + 9 } d x$$

• A) \(\int _ { - \infty } ^ { 2 } \frac { 9 } { x ^ { 2 } + 10 } d x\)
• B) \(\int _ { b } ^ { - \infty } \frac { 10 } { x ^ { 2 } - 9 } d x\)
• C) \(\int _ { - \infty } ^ { b } \frac { 10 } { x ^ { 2 } + 9 } d x\)
• D) \(\int _ { b } ^ { - \infty } \frac { 10 } { x ^ { 2 } + 9 } d x\)
• E) none of these

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Definitions:

Probability

An indicator of the probability that a particular event will happen, denoted as a value ranging from 0 to 1.

Certain Income

refers to money or revenue that is guaranteed or highly likely to be received, with minimal risk of variation or loss.

Fair Insurance Policy

Describes an insurance contract that provide coverage at reasonable, transparent, and equitable terms for both parties.

Uncertainty

The state of having limited knowledge about present or future events, making outcomes unpredictable.