Given code. my main concern is where to place the given variables for the solution. please use code attached **Evaluate the following integral**\[\int_{0}^{4} (1 - e^{-x}) \, dx\]using a single application of the trapezoidal rule.**Choices**- [ ] 1.963369- [ ] 1.36696- [ ] 1.936639- [ ] NoneThe question asks you to evaluate the integral $\int_{0}^{4} (1 - e^{-x}) \, dx$ using the trapezoidal rule. You are given four options to select the correct approximate value of the integral. Below is a Python function that implements the trapezoidal rule for numerical integration with multiple applications:```pythondef Trap(f, x): n = len(x) - 1 s = 0 for i in range(n): f2 = f(x[i+1]) f1 = f(x[i]) s = s + (x[i+1] - x[i]) * (f1 + f2) / 2 #print(s) return s```### Explanation- **Function Definition**: The function `Trap(f, x)` takes two parameters: a function `f` that represents the function to be integrated, and a list `x` that contains the x-coordinates of the points used in the trapezoidal rule.- **Variables**: - `n` is initialized to `len(x) - 1` which represents the number of subintervals. - `s` is initialized to 0, which will accumulate the sum of the areas of the trapezoids.- **Loop**: - The `for` loop iterates over each subinterval. - Within the loop, `f2` and `f1` are calculated as the function values at the endpoints `x[i+1]` and `x[i]`, respectively. - The area of each trapezoid is calculated and added to `s`. The formula `(x[i+1] - x[i]) * (f1 + f2) / 2` computes the area using the average of the two y-values (`f1` and `f2`).- **Return**: - The function returns the accumulated sum `s`, representing the total approximate integral over the interval defined by `x`.

Answer: correct answer is 1.963369 I have done code in python. and attached python code as well as code screenshotPYTHON CODE import numpy as npimport matplotlib.pyplot as pltdef Trap(x): a=0 b=4 h=1 n=int((b-a)/h) s=np.linspace(a,b,n+1) t=np.exp(1-s*s) f=0 for i in range(1,n): f=f+t[i] q=2*f+t[0]+t[n] result=q*(h/2) return resultm=np.linspace(0,4)n=np.zeros(len(m));for i in range(len(n)): n[i]=Trap(m[i])plt.plot(m,n)plt.show()I hope this will meet your requirement and also hope this will help you lot thanks.

Answered: def Trap(f,x): n = len(x)-1; s = 0; for…

Engineering

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def Trap(f,x): n = len(x)-1; s = 0; for i in range (n): f2 = f(x[i+1]); f1=f(x[i]); s = s + (x[i+1]-x[i]) * ( f1+ f2 )/2 #print(s) %3D %3D return s

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Chapter1: Introduction

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Given code. my main concern is where to place the given variables for the solution. please use code attached

**Evaluate the following integral**

\[
\int_{0}^{4} (1 - e^{-x}) \, dx
\]

using a single application of the trapezoidal rule.

**Choices**

- [ ] 1.963369
- [ ] 1.36696
- [ ] 1.936639
- [ ] None

The question asks you to evaluate the integral $\int_{0}^{4} (1 - e^{-x}) \, dx$ using the trapezoidal rule. You are given four options to select the correct approximate value of the integral.

Below is a Python function that implements the trapezoidal rule for numerical integration with multiple applications:

```python
def Trap(f, x):
n = len(x) - 1
s = 0
for i in range(n):
f2 = f(x[i+1])
f1 = f(x[i])
s = s + (x[i+1] - x[i]) * (f1 + f2) / 2
#print(s)
return s
```

### Explanation

- **Function Definition**: The function `Trap(f, x)` takes two parameters: a function `f` that represents the function to be integrated, and a list `x` that contains the x-coordinates of the points used in the trapezoidal rule.

- **Variables**:
- `n` is initialized to `len(x) - 1` which represents the number of subintervals.
- `s` is initialized to 0, which will accumulate the sum of the areas of the trapezoids.

- **Loop**:
- The `for` loop iterates over each subinterval.
- Within the loop, `f2` and `f1` are calculated as the function values at the endpoints `x[i+1]` and `x[i]`, respectively.
- The area of each trapezoid is calculated and added to `s`. The formula `(x[i+1] - x[i]) * (f1 + f2) / 2` computes the area using the average of the two y-values (`f1` and `f2`).

- **Return**:
- The function returns the accumulated sum `s`, representing the total approximate integral over the interval defined by `x`.

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