Answer:
(0,-5)
Step-by-step explanation:
The answer is 1x10^2 or just simply 10^2.
The Jacobian for this transformation is

with determinant
, hence the area element becomes

Then the integral becomes

where
is the unit circle,

so that

Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.

Then

Answer:
Please see explanation for the answer. The code is written in python and is as given below:
Step-by-step explanation:
The solution is obtained on the Python with the following code
import matplotlib.pyplot as plotter
import numpy as npy
x_s = npy.linspace(-5,5,100) #Defining a linear sample space with boundaries as -5 to 5 and 100 as number of samples.
def sigmo(z):return 1/(1 + npy.exp(-z)) #Defining sigmoid function for the f(x).
plotter.plot(x_s, sigmo(x_s))
plotter.plot([-5,5],[.5,.5])
plotter.xlabel("z")
plotter.ylabel("sigmoid(z)")
plotter.show()
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