Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. $\int _ { - \infty } ^ { 0 } e ^ { 6 x } d x$
A)converges to 0
B)converges to 6
C)converges to $\frac { 1 } { 6 }$
D)diverges to $- \infty$
E)diverges to $\infty$

Question

Quizplus · Accepted Answer

The integral converges to $\frac{1}{6}$ because when evaluated, $\int _ { - \infty } ^ { 0 } e ^ { 6 x } d x = \left[ \frac{1}{6} e^{6x} \right]_{-\infty}^{0} = \frac{1}{6} - 0 = \frac{1}{6}$.

Determine Whether the Improper Integral Diverges or Converges ∫−∞0e6xdx\int _ { - \infty } ^ { 0 } e ^ { 6 x } d x∫−∞0​e6xdx

Determine Whether the Improper Integral Diverges or Converges $\int _ { - \infty } ^ { 0 } e ^ { 6 x } d x$