Solve the Problem $y$ -Axis of the Thin Infinite Region of Constant Density

Multiple Choice

Solve the problem.
-Find the moment of inertia about the $y$ -axis of the thin infinite region of constant density $\delta = 3$ in the first quadrant bounded by the coordinate axes and the curve $y = e ^ { - 7 x }$ .

A) $\frac { 9 } { 343 }$
B) $\frac { 1 } { 343 }$
C) $\frac { 6 } { 343 }$
D) $\frac { 3 } { 686 }$