For each t > 0, if \({\rm{\Phi }}\left( {x,t} \right) = \frac{1}{{\sqrt {4\pi t} }}{e^{ - {x^2}/4t}}\) solves the heat equation, then for t > 0

\(\mathop \smallint \limits_{ - \infty }^\infty {\rm{\Phi }}\left( {x,t} \right)dt = \infty\)

\(\mathop \smallint \limits_{ - \infty }^\infty {\rm{\Phi }}\left( {x,t} \right)dt = 0\)

\(\mathop \smallint \limits_{ - \infty }^\infty {\rm{\Phi }}\left( {x,t} \right)dt = 1\)

For each t > 0, if \({\rm{\Phi }}\left( {x,t} \right) = \frac{1}{{\sq

1.	For each t > 0, if \({\rm{\Phi }}\left( {x,t} \right) = \frac{1}{{\sqrt {4\pi t} }}{e^{ - {x^2}/4t}}\) solves the heat equation, then for t > 0
A.	\(\mathop \smallint \limits_{ - \infty }^\infty {\rm{\Phi }}\left( {x,t} \right)dt = 0\)
B.	\(\mathop \smallint \limits_{ - \infty }^\infty {\rm{\Phi }}\left( {x,t} \right)dt = 1\)
C.	\(\mathop \smallint \limits_{ - \infty }^\infty {\rm{\Phi }}\left( {x,t} \right)dt = \infty\)
D.	not defined
Answer» C. \(\mathop \smallint \limits_{ - \infty }^\infty {\rm{\Phi }}\left( {x,t} \right)dt = \infty\)

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For each t > 0, if \({\rm{\Phi }}\left( {x,t} \right) = \frac{1}{{\sqrt {4\pi t} }}{e^{ - {x^2}/4t}}\) solves the heat equation, then for t > 0

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