```python
from sympy import *
from sympy.plotting import plot

x, A, B, T = symbols('x, A, B, T')
B = 2 * pi * (1/T)
kappa = (A*B**2*sin(B*x)) / ((1 + A**2 * B**2 * cos(B*x)**2)**(3/2))
kappa = abs(kappa)
kappa
```




$\displaystyle 4 \pi^{2} \left|{\frac{A \sin{\left(\frac{2 \pi x}{T} \right)}}{T^{2} \left(\frac{4 \pi^{2} A^{2} \cos^{2}{\left(\frac{2 \pi x}{T} \right)}}{T^{2}} + 1\right)^{1.5}}}\right|$




```python
subs = {}
subs['T'] = 15
subs['A'] = 6
subs['x'] = 15/4
kappa.evalf(subs=subs)
```




$\displaystyle 1.05275780278287$




```python
integral = Integral(kappa, (x, 0, 15))
integral
```




$\displaystyle \int\limits_{0}^{15} 4 \pi^{2} \left|{\frac{A \sin{\left(\frac{2 \pi x}{T} \right)}}{T^{2} \left(\frac{4 \pi^{2} A^{2} \cos^{2}{\left(\frac{2 \pi x}{T} \right)}}{T^{2}} + 1\right)^{1.5}}}\right|\, dx$




```python
subs = {}
subs['T'] = 15
subs['A'] = 6
integral.subs(subs).evalf()
```




$\displaystyle 3.7166$




```python
3.7166 / 15
```




    0.24777333333333335




```python
_ = plot(kappa.subs(subs), (x, 0, 15))
```


```python

```

9b78df9173e0603e650db7b3896f2fb471f08915
ipynb
Jupyter Notebook
Analysis/Notebooks/Sine Curve Dataset/Integration.ipynb
brouhardlab/kappa
2e74530e54fc02e08e03e56a4a33ece6c7ce9941
MIT
2017-11-29T15:09:50.000Z
2020-12-04T11:08:17.000Z
Analysis/Notebooks/Sine Curve Dataset/Integration.ipynb
brouhardlab/kappa
2e74530e54fc02e08e03e56a4a33ece6c7ce9941
MIT
2017-11-17T19:20:10.000Z
2020-08-16T16:33:31.000Z
Analysis/Notebooks/Sine Curve Dataset/Integration.ipynb
brouhardlab/kappa
2e74530e54fc02e08e03e56a4a33ece6c7ce9941
MIT
2017-10-13T02:24:17.000Z
2022-03-16T01:14:59.000Z
Qwen/Qwen-72B
1. YES
2. YES