Integration, Symbolic and Numeric with Python

[xx]

Good video, just not what I was hoping for
Just in case anyone was hoping this video would be about numeric integration in python, not importing scripts in python, here's an actual numeric code:
# example function
def func(x):
y = 1
y = (x*x*x) - (2*(x*x)) + x - 3
return y

# Integrate function
def integrate(start, end, step):
result = 1
index = start
while(index <= end):
result = result + func(index)
index = index + step
result = result * step
return result

def main():
print(integrate(-2, 2, 0.001))

main()

[hamedjabarian]

Very helpful, articulated and practical examples just in very low time. Thanks

[matrixate]

Wow. My Python Professor needs to take lessons from you. Seriously. I've spent weeks studying from her and it's a bunch of guessing and anticipating and not clearly explained as this. My grant payers should get a refund.

[gillespieQMA]

Thanks so much! Right to the point and practical!

[noobmaster-dmtu]

thanks for this
could you touch upon the difference between using quad and trapzd for integration?

[kiranshakeel]

Hi thats a great video.Could you please tell if there are double integrals and dx, dy, how to deal with that in python?

[Vathananable]

Can you integrate with Python to find volume?

[johanmoens]

Top video! Is Matlab good in solving the more complex integrals?

[sriharshakodati]

This is great. May I ask a query. When we use sympy for analytical solution for an integration, sometimes the output seem to be a piecewise datatype. May I know how to resolve this?
Example:
from sympy import *
x=Symbol('x')
alpha=Symbol('alpha')
beta=Symbol('beta')
W=Symbol('W')
f1=(alpha-beta)
result1=integrate(f1, (x, 0, x))
f2=alpha*exp(-result1)
result2=integrate(f2, (x, 0, W))
M=1/(1-result2)
print(M)
Output: 1/(1 - Piecewise((alpha/(alpha - beta) - alpha*exp(-W*(alpha - beta))/(alpha - beta), Ne(alpha - beta, 0)), (W*alpha, True)))

[ayanmitra]

Hi great video, short and crisp. thanks. I have another question, if you would help will be great. If I have x & y column data, can you tell how can I integrate them [with y = int f(x) ]?
thanks
A M

[rookitchen]

I'm not a coder person. I need to output a bunch of anti derivatives as training data. I can't afford mathematica, so Im using jupytor with python 3 in my browser. I havent found a way to get wolfram alpha to output lists of antiderivatives like I want. My code only outputs one integral at a time. I thought maybe doing like a print(sp.integrate(x*sin(x**2), x), but I don't like its non-nice form. How can I get it to output a list of antideriviatives? My code:
import sympy as sp
from sympy import sin, cos, exp, log, simplify
x = sp.Symbol('x')
sp.integrate(x*sin(x**2), x)
sp.integrate(x, x)
The problem is that in the output, you can only see the last integral. So I try to do a print thing and then the outputs are no longer user friendly.
import sympy as sp
from sympy import sin, cos, exp, log, simplify
x = sp.Symbol('x')
print(sp.integrate(x*sin(x**2), x)
, sp.integrate(x, x))
I'll prolly figure it out before you get back to me, but figure Id put out a feeler.

[kuncheng]

It's pretty helpful, Thank you. Is it possible to integrate a function with a singularity and get a result consisting of the real and imaginary parts?

[francescodallevedove]

Hi nice video, but what about if I have a function to be integrated that has variable coefficient: f(w, t) = b(w)*cos(w*t).
b(w) comes from a data base and let's say w(0, 5, 0.05) and we want F(t) = int f(w, t)) dw?

[ThomasJr]

DEEPLY DISAPPOINTED WITH THIS PACKAGE. IT CAN'T INTEGRATE A FUNCTION THAT MATHEMATICA INTEGRATES BETTER AND FASTER. I TRIED IT THINKING IT WOULD BE A STEP UP FROM MATHEMATICA, BUT IT'S NOT SO.
*Here the code.*

q=3/2
n=2

def f(u):
return

exp = quad(f, 0, 1)

*Am I doing something wrong?*

[hamzaa.]

Thank you. Please magnify the screen a bit.

[rohanarya]

Hi,
Very well demonstrated. Thanks for the examples.
I had a question with complex integrations. Is it impossible to derive symbolic expressions of integral like x/(1+0.000015x^2)? I keep getting the error "no convergence : try value of n<30 and maxsteps > 50. I tried changing these values too but no luck. Kindly, guide where I am wrong .

[kedwards]

Thank you so much this was extremely helpful!!

[allaniamed]

how i can make global assumption assume(x>3) so when i tape abs(x-3) i get x-3 and thxs

[NZIT]

Hi ApMonitor.com. Let's me start to give you thanks for the so wonderful explications regarding analytical and numerical way to solve integration using Python code. However I want just to mention one thing about the famous exercise to gave us to solve . (integral of exp^(-x)sin(3x)dx. For the analytical part you found zero as answer for that integration something I didn't understood, I tried it myself I got the answer which is different to zero. I was wondering why did we not get the same answer? Have you some reason for that? Thanks a lot .

[yellowsmash]

i am failing to apply integration help me f (x) = 20 e -20(x-12.5),
limits (12.6 to infinity), (12.5 to 12.6) i want python code
i tried d=12.6
sp.integrate(sp.exp(-20*(d-12.5)), y)
output:0.135335283236614𝑦