A) See the attached graph. The purple area appears to be what you want to find.
b) Integrating with respect to x seems much easier. If one were to integrate over y, there would need to be two regions of integration: [1, e^2] and [e^2, e^4].
c)
You have to turn them in to the lowest common denominator
The distance formula for two points in a plane is
D=sqrt( (x1-x2)^2 + (y1-y2)^2 )
From T to U
D= sqrt((80-20)^2 + (20-60)^2) = 72.11
Then flying from U to V
D= sqrt((20-110)^2 + (60-85)^2) = 93.4
So T to U to V = 72.11+93.4 = 165.5
BUT checking also T to V to U
From T to V
D= sqrt((80-110)^2 + (20-85)^2) = 71.6
Then from V to U
D= sqrt((110-20)^2 + (85-60)^2) = 93.4
So from T to V to U = 165
Pretty much the same both directions
So yes the answer is A
I’m not 100% sure but I think it’s D.