Solve the problem.
-Evaluate
$$\int _ { 0 } ^ { \infty } \frac { \sin x } { x } d x$$
by integrating
$$\int _ { 0 } ^ { \infty } \int _ { 0 } ^ { \infty } e ^ { - x y } \sin x d A$$
A) $\frac { \pi } { 3 }$
B) $\frac { \pi } { 6 }$
C) $\frac { \pi } { 2 }$
D) $\frac { \pi } { 4 }$

Question

Quizplus · Accepted Answer

The integral $\int _ { 0 } ^ { \infty } \frac { \sin x } { x } d x$ is a known result called the Dirichlet integral, which evaluates to $\frac{\pi}{2}$. This can be shown by using the double integral technique and Fubini's theorem to switch the order of integration.

Solve the Problem ∫0∞sin⁡xxdx\int _ { 0 } ^ { \infty } \frac { \sin x } { x } d x∫0∞​xsinx​dx

Solve the Problem $\int _ { 0 } ^ { \infty } \frac { \sin x } { x } d x$