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) \(\sqrt { 5 \pi }\)

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Definitions:

Demand

The amount of a product or service that buyers are ready and capable of buying at different price levels over a specified time frame.

Increase

A situation where there is a growth or rise in figures, amounts, or indicators in an economic context.

Demand Curve

A graphical representation that shows the relationship between the price of a good and the quantity demanded by consumers.

Demand

The quantity of a good or service that consumers are willing and able to purchase at various prices during a given period.