Determine Whether the Improper Integral $\int _ { - \infty } ^ { \infty } \frac { 9 } { 49 + x ^ { 2 } } d x$

question 85

Multiple Choice

Determine whether the improper integral $\int _ { - \infty } ^ { \infty } \frac { 9 } { 49 + x ^ { 2 } } d x$ diverges or converges. Evaluate the integral if it converges.

• A) \(\frac { 9 } { 49 }\)
• B) \(\frac { 9 } { 7 } \pi\)
• C) \(\frac { 9 } { 49 } \pi\)
• D) \(\frac { 9 } { 7 }\)
• E) diverges

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Definitions:

Free Association

A psychoanalytic technique where patients are encouraged to verbalize thoughts as they come, without censorship, to uncover unconscious desires or issues.

Verbalize

To verbalize means to express thoughts or feelings in words, making abstract concepts communicable and understandable.

Frightening

Causing fear or alarm; having the ability to induce fear or a sense of dread.

Psychodynamic Therapy

A therapeutic approach emphasizing the psychological root causes of emotional suffering, primarily focuses on unconscious processes as they are manifested in a person's present behavior.