Romberg integration in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the Romberg integration function from scipy.

SciPy

from scipy.integrate import [1]

Drag options to blanks, or click blank then click option'

Aromberg

Btrapz

Cquad

Dsimps

Attempts:

3 left

💡 Hint

Common Mistakes

Importing quad instead of romberg.

Using integration functions unrelated to Romberg.

The romberg function is used for Romberg integration in scipy.

2fill in blank

medium

Complete the code to define the function f(x) = x^2 for integration.

SciPy

def f(x):
    return x[1]2

Drag options to blanks, or click blank then click option'

A+

B**

C*

D//

Attempts:

3 left

💡 Hint

Common Mistakes

Using * instead of ** for power.

Using + or // which are incorrect here.

The ** operator is used for exponentiation in Python.

3fill in blank

hard

Fix the error in calling romberg to integrate f from 0 to 1.

SciPy

result = romberg(f, [1], 1)

Drag options to blanks, or click blank then click option'

A1

Bf

C0

D2

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping the limits or passing the function instead of a limit.

Using 1 as the first limit which is the upper limit.

The integration lower limit is 0, so it must be the first argument after the function.

4fill in blank

hard

Fill both blanks to compute Romberg integration of sin(x) from 0 to pi.

SciPy

import numpy as np
result = romberg(np.[1], 0, [2])

Drag options to blanks, or click blank then click option'

Asin

Bcos

Cnp.pi

De

Attempts:

3 left

💡 Hint

Common Mistakes

Using cosine instead of sine.

Using e instead of pi as upper limit.

We integrate sin from 0 to pi (np.pi).

5fill in blank

hard

Fill all three blanks to create a dictionary of Romberg results for functions over [0, 1].

SciPy

functions = {'square': lambda x: x[1]2, 'cube': lambda x: x[2]3}
results = {name: romberg(func, 0, 1) for name, func in functions.items() if func(0) == [3]

Drag options to blanks, or click blank then click option'

A**

B*

C0

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication * instead of exponentiation **.

Checking if function(0) equals 1 instead of 0.

Use ** for powers and check if function value at 0 equals 0.