Nugroho's blog.: Numeric Integration using Python and Pylab

## Friday, April 14, 2017

### Numeric Integration using Python and Pylab

Pylab is Python module that contain NumPy and MatPlotlib.

Let f(x) = x^2 and we want to integrate it from 0 to 1.

Numerically we could use square method or trapezoidal (which is almost better).

Let use square method first.

and count "inner square" using this code

```from pylab import *

def f(x):
return x*x

def integrate(x):
sum = 0
for i in arange(len(x)-1):
sum += f(x[i])*dx
return sum

x   = linspace(0,1,100)
dx  = x-x
y   = f(x)
print integrate(x)
plot(x,y)
grid(True)
show()

```

The result is 0.32829983335.

The  "outer square "  code below give the result 0.338400843451

```from pylab import *

def f(x):
return x*x

def integrate(x):
sum = 0
for i in arange(len(x)-1):
sum += f(x[i+1])*dx
return sum

x   = linspace(0,1,100)
dx  = x-x
y   = f(x)
print integrate(x)
plot(x,y)
grid(True)
show()
```

How about Trapezoidal method? Easy, just modify little bit, and give the result 0.333350338401,  which is much better,  :)

```from pylab import *
```

```def f(x):
return x*x

def integrate(x):
sum = 0
for i in arange(len(x)-1):
sum += (f(x[i])+f(x[i+1]))*dx/2.
return sum

x   = linspace(0,1,100)
dx  = x-x
y   = f(x)
print integrate(x)
plot(x,y)
grid(True)
show()```
.