Solve the Problem $$\int _ { 0 } ^ { \infty } e ^ { - x ^ { 2 } } d x = \frac { \sqrt { \pi } } { 2 } ,$$

question 102

Multiple Choice

Solve the problem.
-Given that
$$\int _ { 0 } ^ { \infty } e ^ { - x ^ { 2 } } d x = \frac { \sqrt { \pi } } { 2 } ,$$
evaluate
$$\int _ { 0 } ^ { \infty } e ^ { - 5 x ^ { 2 } } d x$$

• A) \(\frac { 1 } { 2 } \sqrt { \frac { \pi } { 5 } }\)
• B) \(\frac { 1 } { 2 } \sqrt { 5 \pi }\)
• C) \(\sqrt { \frac { \pi } { 5 } }\)
• D) \(\sqrt { 5 \pi }\)

---

Definitions:

Kinship

Social bonds and relationships derived from blood ties, marriage, or adoption, forming the basic units of social organization.

Shared Citizenship

A concept where individuals hold citizenship in more than one country, enjoying legal rights and responsibilities in each.

Obligation

A moral or legal duty to perform or not perform a certain action.

Drowning Child Scenario

A hypothetical ethical dilemma used to discuss moral obligations and altruism, asking what duties one has to rescue a child in immediate danger when doing so is at little cost to oneself.