Answer:
As per the given statement:
The region bounded by the given curves about the y-axis,
, y=0, x = 0 and x = 1
Using cylindrical shell method:
The volume of solid(V) is obtained by rotating about y-axis and the region under the curve y = f(x) from a to b is;
where 
where x is the radius of the cylinder
f(x) is the height of the cylinder.
From the given figure:
radius = x
height(h) =f(x) =y=
a = 0 and b = 1
So, the volume V generated by rotating the given region:
![V =2 \pi \int_{0}^{1} x ( 13e^{-x^2}) dx\\\\V=2\pi\left [ -\frac{13}{2}e^{-x^2} \right ]_{0}^{1}\\\\V=2\pi\left (-\frac{13}{2e}-\left(-\frac{13}{2}\right) \right )\\\\V=-\frac{13\pi }{e}+13\pi](https://tex.z-dn.net/?f=V%20%3D2%20%5Cpi%20%5Cint_%7B0%7D%5E%7B1%7D%20x%20%28%2013e%5E%7B-x%5E2%7D%29%20dx%5C%5C%5C%5CV%3D2%5Cpi%5Cleft%20%5B%20-%5Cfrac%7B13%7D%7B2%7De%5E%7B-x%5E2%7D%20%5Cright%20%5D_%7B0%7D%5E%7B1%7D%5C%5C%5C%5CV%3D2%5Cpi%5Cleft%20%28-%5Cfrac%7B13%7D%7B2e%7D-%5Cleft%28-%5Cfrac%7B13%7D%7B2%7D%5Cright%29%20%5Cright%20%29%5C%5C%5C%5CV%3D-%5Cfrac%7B13%5Cpi%20%7D%7Be%7D%2B13%5Cpi%20)
therefore, the volume of V generated by rotating the given region is 
As given,
Loan amount is = $45000
Rate of interest = 8.5%
So, Tony's mortgage will attract an interest of:
= $3825 (this is yearly)
And for 1st month it will be =
= $318.75
As given, the first month's payment is $390.60 and this covers the interest Additional amount ($390.60 - $318.75 = $71.85) is a payment against the principle.
Hence, the new principle after the 1st month is $71.85 less than $45000
= 45000-71.85 = $44928.15
Hence, the last option $44928.15 is the correct answer.