AP CALC AB problem (high school)

1)

f(x) = e^(-x/4) + sin (x^2), g(x) = (1/3)x^2 - x, and x-axis supposedly create a region where I am to find the area/perimeter/volume. When I graph this, there is no region such that satisfies the condition of all 3. Am I graphing this incorrectly? or is this AP calculus AB question just poorly/incorrectly written?

2)

g(x) = (5 e^(-x/6) ) (sin ((x^2) / 6)) and the x-axis enclose a region R. Again, I'm supposed to find area/perimeter/volume.

I am pretty sure the region R enclosed by g(x) and the x-axis is infinite as it goes on and on and on...which would set up an infinite amounts of integral [x1,x2] + integral [x2,x3] + etc as the upper and lower bounds keep alternating due to the sin wave of the function.

plot (5e^(-x/6))(sin((x^2) 7;6)) - Wolfram|Alpha

no domain was specified. I doubt the teacher meant to trick high school students with this. Am I looking at these two questions wrong? Thanks!