Consider the integral $I = \int _ { 1 } ^ { \infty } e ^ { a x ^ { 2 } + b x + c } d x$, where $a , b , c$ are constants. Some combinations of values for these constants are given below and you have to decide in each case whether the integral $I$ converges. (A) $I$ converges for $a = - 1 \quad b = 10 \quad c = 100$. (B) $I$ converges for $a = 1 \quad b = - 10 \quad c = - 100$. (C) $I$ converges for $a = 0 \quad b = - 1 \quad c = 100$. (D) $I$ converges for $a = 0 \quad b = 0 \quad c = - 100$.
Consider the integral $I = \int _ { 1 } ^ { \infty } e ^ { a x ^ { 2 } + b x + c } d x$, where $a , b , c$ are constants. Some combinations of values for these constants are given below and you have to decide in each case whether the integral $I$ converges.\\
(A) $I$ converges for $a = - 1 \quad b = 10 \quad c = 100$.\\
(B) $I$ converges for $a = 1 \quad b = - 10 \quad c = - 100$.\\
(C) $I$ converges for $a = 0 \quad b = - 1 \quad c = 100$.\\
(D) $I$ converges for $a = 0 \quad b = 0 \quad c = - 100$.