$\text { Determine whether the improper integral } \int _ { 0 } ^ { \infty } e ^ { - 3 x } \sin ( 3 x ) d x \text { diverges or converges. }$ Evaluate the integral if it converges.
A) 18
B) 9
C) $\frac { 1 } { 6 }$
D) 3
E) diverges

Question

$\text { Determine whether the improper integral } \int _ { 0 } ^ { \infty } e ^ { - 3 x } \sin ( 3 x ) d x \text { diverges or converges. }$ Evaluate the integral if it converges. 
A) 18
B) 9
C) $\frac { 1 } { 6 }$
D) 3
E) diverges

Quizplus · Accepted Answer

The integral converges and can be evaluated using integration by parts twice, leading to a fraction $\frac{1}{6}$.