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

question 93

Multiple Choice

Solve the problem.
-Given that
$$\int _ { 0 } ^ { \infty } \mathrm { e } ^ { - \mathrm { x } ^ { 2 } } \mathrm { dx } = \frac { \sqrt { \pi } } { 2 } ,$$
evaluate
$$\int _ { - \infty } ^ { \infty } e ^ { - 6 x ^ { 2 } } d x$$

• A) \(\frac { 1 } { 2 } \sqrt { 6 \pi }\)
• B) \(\sqrt { \frac { \pi } { 6 } }\)
• C) \(\sqrt { 6 \pi }\)
• D) \(\frac { 1 } { 2 } \sqrt { \frac { \pi } { 6 } }\)

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