How to integrate Simpsons rule using Scipy to plot a 1D graph

i need some help, i have an assignment to code an integration of a function using simpsons rule. I need to use the inbuilt scipy integratesimps function to plot a 1D graph. I just don't know where to start. I think i have to get a list/array of each value of y for the function that corresponds to each values of x: e.g

if my function is x^2
then when
x is 0 y is 0,
x is 1 y is 1,
x is 2 y is 4,
and so on up to a huge limit...

and then use integrate.simps(y,x) where y are all the y values as shown above and x are all the corresponding x values.

However, i can't get it to work at all...has anyone got any examples of a graph plot for a function of x^2 using integrate.simps(y,x)?

here is what i've got so far:

import numpy as np

from scipy import integrate

import matplotlib.pyplot as plt



x = np.linspace(-10,10,N)

N = 100



yarray = 



def f(x):

    return x**2



for i in x :

    y = f(i)

    yarray.append(y)



print(yarray)





E = integrate.simps(yarray,x)

print(E)



plt.plot(x,E)

asked Nov 20 '18 at 0:55

M.B

What do you mean by plotting a 1D graph, are you trying to plot x^2, the integration of x^2, or something else?

– William Lee
Nov 20 '18 at 1:22

i'm trying to plot the integration of x^2, using the integrate.simps()

– M.B
Nov 20 '18 at 1:49

add a comment |

if my function is x^2
then when
x is 0 y is 0,
x is 1 y is 1,
x is 2 y is 4,
and so on up to a huge limit...

and then use integrate.simps(y,x) where y are all the y values as shown above and x are all the corresponding x values.

However, i can't get it to work at all...has anyone got any examples of a graph plot for a function of x^2 using integrate.simps(y,x)?

here is what i've got so far:

import numpy as np

from scipy import integrate

import matplotlib.pyplot as plt



x = np.linspace(-10,10,N)

N = 100



yarray = 



def f(x):

    return x**2



for i in x :

    y = f(i)

    yarray.append(y)



print(yarray)





E = integrate.simps(yarray,x)

print(E)



plt.plot(x,E)

asked Nov 20 '18 at 0:55

M.B

What do you mean by plotting a 1D graph, are you trying to plot x^2, the integration of x^2, or something else?

– William Lee
Nov 20 '18 at 1:22

i'm trying to plot the integration of x^2, using the integrate.simps()

– M.B
Nov 20 '18 at 1:49

add a comment |

if my function is x^2
then when
x is 0 y is 0,
x is 1 y is 1,
x is 2 y is 4,
and so on up to a huge limit...

and then use integrate.simps(y,x) where y are all the y values as shown above and x are all the corresponding x values.

However, i can't get it to work at all...has anyone got any examples of a graph plot for a function of x^2 using integrate.simps(y,x)?

here is what i've got so far:

import numpy as np

from scipy import integrate

import matplotlib.pyplot as plt



x = np.linspace(-10,10,N)

N = 100



yarray = 



def f(x):

    return x**2



for i in x :

    y = f(i)

    yarray.append(y)



print(yarray)





E = integrate.simps(yarray,x)

print(E)



plt.plot(x,E)

asked Nov 20 '18 at 0:55

M.B

if my function is x^2
then when
x is 0 y is 0,
x is 1 y is 1,
x is 2 y is 4,
and so on up to a huge limit...

and then use integrate.simps(y,x) where y are all the y values as shown above and x are all the corresponding x values.

However, i can't get it to work at all...has anyone got any examples of a graph plot for a function of x^2 using integrate.simps(y,x)?

here is what i've got so far:

import numpy as np

from scipy import integrate

import matplotlib.pyplot as plt



x = np.linspace(-10,10,N)

N = 100



yarray = 



def f(x):

    return x**2



for i in x :

    y = f(i)

    yarray.append(y)



print(yarray)





E = integrate.simps(yarray,x)

print(E)



plt.plot(x,E)

python scipy numerical-methods integral simpsons-rule

asked Nov 20 '18 at 0:55

M.B

asked Nov 20 '18 at 0:55

M.B

asked Nov 20 '18 at 0:55

M.B

asked Nov 20 '18 at 0:55

M.B

asked Nov 20 '18 at 0:55

M.B

What do you mean by plotting a 1D graph, are you trying to plot x^2, the integration of x^2, or something else?

– William Lee
Nov 20 '18 at 1:22

i'm trying to plot the integration of x^2, using the integrate.simps()

– M.B
Nov 20 '18 at 1:49

add a comment |

What do you mean by plotting a 1D graph, are you trying to plot x^2, the integration of x^2, or something else?

– William Lee
Nov 20 '18 at 1:22

i'm trying to plot the integration of x^2, using the integrate.simps()

– M.B
Nov 20 '18 at 1:49

What do you mean by plotting a 1D graph, are you trying to plot x^2, the integration of x^2, or something else?

– William Lee
Nov 20 '18 at 1:22

i'm trying to plot the integration of x^2, using the integrate.simps()

– M.B
Nov 20 '18 at 1:49

add a comment |

1 Answer
1

active

oldest

votes

Basically, you need to calculate the integral value for every range of x, from [-10,-10] to [-10,10]

This example code plots

enter image description here

import numpy as np

from scipy import integrate

import matplotlib.pyplot as plt



def f(x):

    return x**2



N = 100

x = np.linspace(-10,10,N)





integrals = 

x_range = 

y_range = 

for i in x:

    x_range.append(i)

    y_range.append(f(i))

    integral = integrate.simps(y_range, x_range)

    integrals.append(integral)



plt.plot(x, integrals)

plt.show()

To wrap it up

import numpy as np

from scipy import integrate

import matplotlib.pyplot as plt



def integrals(f, xs):

    x_range = 

    y_range = 

    results = 

    for x in xs:

        x_range.append(x)

        y_range.append(f(x))

        integral = integrate.simps(y_range, x_range)

        results.append(integral)

    return results



def f(x, b):

    return (x-b)**2



xs = np.linspace(-10, 10, 100)



plt.plot(xs, integrals(lambda x: f(x, 0), xs), label='b=0')

plt.plot(xs, integrals(lambda x: f(x, 2), xs), label='b=2')

plt.plot(xs, integrals(lambda x: f(x, 4), xs), label='b=4')

plt.title('$y(x) = int_{-10}^{x}(t-b)^2dt$')

plt.xlabel('x')

plt.ylabel('y')

plt.legend()

plt.show()

and you get enter image description here

edited Nov 20 '18 at 12:15

answered Nov 20 '18 at 4:01

William Lee

187110

Thanks! that works really well, what happens if i have a variable in my function? e.g (x-b)^2 where b is changing

– M.B
Nov 20 '18 at 11:50

add a comment |

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1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

Basically, you need to calculate the integral value for every range of x, from [-10,-10] to [-10,10]

This example code plots

enter image description here

import numpy as np

from scipy import integrate

import matplotlib.pyplot as plt



def f(x):

    return x**2



N = 100

x = np.linspace(-10,10,N)





integrals = 

x_range = 

y_range = 

for i in x:

    x_range.append(i)

    y_range.append(f(i))

    integral = integrate.simps(y_range, x_range)

    integrals.append(integral)



plt.plot(x, integrals)

plt.show()

To wrap it up

import numpy as np

from scipy import integrate

import matplotlib.pyplot as plt



def integrals(f, xs):

    x_range = 

    y_range = 

    results = 

    for x in xs:

        x_range.append(x)

        y_range.append(f(x))

        integral = integrate.simps(y_range, x_range)

        results.append(integral)

    return results



def f(x, b):

    return (x-b)**2



xs = np.linspace(-10, 10, 100)



plt.plot(xs, integrals(lambda x: f(x, 0), xs), label='b=0')

plt.plot(xs, integrals(lambda x: f(x, 2), xs), label='b=2')

plt.plot(xs, integrals(lambda x: f(x, 4), xs), label='b=4')

plt.title('$y(x) = int_{-10}^{x}(t-b)^2dt$')

plt.xlabel('x')

plt.ylabel('y')

plt.legend()

plt.show()

and you get enter image description here

edited Nov 20 '18 at 12:15

answered Nov 20 '18 at 4:01

William Lee

187110

Thanks! that works really well, what happens if i have a variable in my function? e.g (x-b)^2 where b is changing

– M.B
Nov 20 '18 at 11:50

add a comment |

Basically, you need to calculate the integral value for every range of x, from [-10,-10] to [-10,10]

This example code plots

enter image description here

import numpy as np

from scipy import integrate

import matplotlib.pyplot as plt



def f(x):

    return x**2



N = 100

x = np.linspace(-10,10,N)





integrals = 

x_range = 

y_range = 

for i in x:

    x_range.append(i)

    y_range.append(f(i))

    integral = integrate.simps(y_range, x_range)

    integrals.append(integral)



plt.plot(x, integrals)

plt.show()

To wrap it up

import numpy as np

from scipy import integrate

import matplotlib.pyplot as plt



def integrals(f, xs):

    x_range = 

    y_range = 

    results = 

    for x in xs:

        x_range.append(x)

        y_range.append(f(x))

        integral = integrate.simps(y_range, x_range)

        results.append(integral)

    return results



def f(x, b):

    return (x-b)**2



xs = np.linspace(-10, 10, 100)



plt.plot(xs, integrals(lambda x: f(x, 0), xs), label='b=0')

plt.plot(xs, integrals(lambda x: f(x, 2), xs), label='b=2')

plt.plot(xs, integrals(lambda x: f(x, 4), xs), label='b=4')

plt.title('$y(x) = int_{-10}^{x}(t-b)^2dt$')

plt.xlabel('x')

plt.ylabel('y')

plt.legend()

plt.show()

and you get enter image description here

edited Nov 20 '18 at 12:15

answered Nov 20 '18 at 4:01

William Lee

187110

Thanks! that works really well, what happens if i have a variable in my function? e.g (x-b)^2 where b is changing

– M.B
Nov 20 '18 at 11:50

add a comment |

Basically, you need to calculate the integral value for every range of x, from [-10,-10] to [-10,10]

This example code plots

enter image description here

import numpy as np

from scipy import integrate

import matplotlib.pyplot as plt



def f(x):

    return x**2



N = 100

x = np.linspace(-10,10,N)





integrals = 

x_range = 

y_range = 

for i in x:

    x_range.append(i)

    y_range.append(f(i))

    integral = integrate.simps(y_range, x_range)

    integrals.append(integral)



plt.plot(x, integrals)

plt.show()

To wrap it up

import numpy as np

from scipy import integrate

import matplotlib.pyplot as plt



def integrals(f, xs):

    x_range = 

    y_range = 

    results = 

    for x in xs:

        x_range.append(x)

        y_range.append(f(x))

        integral = integrate.simps(y_range, x_range)

        results.append(integral)

    return results



def f(x, b):

    return (x-b)**2



xs = np.linspace(-10, 10, 100)



plt.plot(xs, integrals(lambda x: f(x, 0), xs), label='b=0')

plt.plot(xs, integrals(lambda x: f(x, 2), xs), label='b=2')

plt.plot(xs, integrals(lambda x: f(x, 4), xs), label='b=4')

plt.title('$y(x) = int_{-10}^{x}(t-b)^2dt$')

plt.xlabel('x')

plt.ylabel('y')

plt.legend()

plt.show()

and you get enter image description here

edited Nov 20 '18 at 12:15

answered Nov 20 '18 at 4:01

William Lee

187110

Basically, you need to calculate the integral value for every range of x, from [-10,-10] to [-10,10]

This example code plots

enter image description here

import numpy as np

from scipy import integrate

import matplotlib.pyplot as plt



def f(x):

    return x**2



N = 100

x = np.linspace(-10,10,N)





integrals = 

x_range = 

y_range = 

for i in x:

    x_range.append(i)

    y_range.append(f(i))

    integral = integrate.simps(y_range, x_range)

    integrals.append(integral)



plt.plot(x, integrals)

plt.show()

To wrap it up

import numpy as np

from scipy import integrate

import matplotlib.pyplot as plt



def integrals(f, xs):

    x_range = 

    y_range = 

    results = 

    for x in xs:

        x_range.append(x)

        y_range.append(f(x))

        integral = integrate.simps(y_range, x_range)

        results.append(integral)

    return results



def f(x, b):

    return (x-b)**2



xs = np.linspace(-10, 10, 100)



plt.plot(xs, integrals(lambda x: f(x, 0), xs), label='b=0')

plt.plot(xs, integrals(lambda x: f(x, 2), xs), label='b=2')

plt.plot(xs, integrals(lambda x: f(x, 4), xs), label='b=4')

plt.title('$y(x) = int_{-10}^{x}(t-b)^2dt$')

plt.xlabel('x')

plt.ylabel('y')

plt.legend()

plt.show()

and you get enter image description here

edited Nov 20 '18 at 12:15

answered Nov 20 '18 at 4:01

William Lee

187110

edited Nov 20 '18 at 12:15

answered Nov 20 '18 at 4:01

William Lee

187110

answered Nov 20 '18 at 4:01

William Lee

187110

answered Nov 20 '18 at 4:01

William Lee

187110

Thanks! that works really well, what happens if i have a variable in my function? e.g (x-b)^2 where b is changing

– M.B
Nov 20 '18 at 11:50

add a comment |

Thanks! that works really well, what happens if i have a variable in my function? e.g (x-b)^2 where b is changing

– M.B
Nov 20 '18 at 11:50

Thanks! that works really well, what happens if i have a variable in my function? e.g (x-b)^2 where b is changing

– M.B
Nov 20 '18 at 11:50

add a comment |

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