Looks like you have most of the details already, but you're missing one crucial piece.
is parameterized by
for 
and 
, and a normal vector to this surface is
with norm
So the integral of 
is
Answer:
B and E
Step-by-step explanation:
For perimeter you add up the two sides so 15 + 21 equals 36
Answer:
g(x) = 4x² -x +64
Step-by-step explanation:
The integral of f(x) will be continuous. This means the value must be the same for x = 4- as for x = 4+.
For some constant c1, the integral in the region x ≤ 4 is ...
∫f(x)dx = (4x² -x +c1) +C = g(x) +C
The integral in the region x ≥ 4 is given as ...
∫f(x)dx = 31x +C
Evaluated at x=4, we must get the same value from either expression:
4(4²) -4 +c1 +C = 31(4) +C
60 +c1 = 124
c1 = 64
__
In order to make the integral continuous at x=4, we must have ...
g(x) = 4x² -x +64
