## Integrating equations in python

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A common need in engineering calculations is to integrate an equation over some range to determine the total change. For example, say we know the volumetric flow changes with time according to $$d\nu/dt = \alpha t$$, where $$\alpha = 1$$ L/min and we want to know how much liquid flows into a tank over 10 minutes if the volumetric flowrate is $$\nu_0 = 5$$ L/min at $$t=0$$. The answer to that question is the value of this integral: $$V = \int_0^{10} \nu_0 + \alpha t dt$$.

import scipy
from scipy.integrate import quad

nu0 = 5     # L/min
alpha = 1.0 # L/min
def integrand(t):
return nu0 + alpha * t

t0 = 0.0
tfinal = 10.0
V, estimated_error = quad(integrand, t0, tfinal)
print('{0:1.2f} L flowed into the tank over 10 minutes'.format(V))

100.00 L flowed into the tank over 10 minutes


That is all there is too it!

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