It is hard to comprehend your question. As far as I understand:
f(x,y) = e^(-x)
Find the volume over region R = {(x,y): 0<=x<=ln(6), -6<=y <= 6}.
That is all I understood. It would be easier to understand with a picture or some kind of visual aid.
Anyways, to find the volume between the surface and your rectangular region R, we must evaluate a double integral of f on the region R.

Now evaluate,

which evaluates to, 5/6 if I did the math correct. Correct me if I am wrong.
Now integrate this w.r.t. y:

So,

The equation that matches the graph is the second one !
Another way to say f(x) is y, so y=0 at -2 and 10. :)
There are seven letters in the word "FREEZER"
so, it would be: ⁷P⁶ = 7! / (7-6)! = 7! / 1!
= 7 * 6 * 5 * 4 * 3 * 2
= 5040
In short, Your Answer would be 5040
Hope this helps!
Answer:
a:-2
Step-by-step explanation: