Triple integral (tplquad) in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the function for triple integration from scipy.

SciPy

from scipy.integrate import [1]

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Atplquad

Bnquad

Cdblquad

Dquad

Attempts:

3 left

💡 Hint

Common Mistakes

Using dblquad which is for double integrals.

Using quad which is for single integrals.

The tplquad function is used for triple integrals in scipy.

2fill in blank

medium

Complete the code to define the function f(x, y, z) = x * y * z for integration.

SciPy

def f(x, y, z):
    return [1]

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Ax + y + z

Bx / (y + z)

Cx - y - z

Dx * y * z

Attempts:

3 left

💡 Hint

Common Mistakes

Adding variables instead of multiplying.

Using division which is not the function defined.

The function to integrate is the product of x, y, and z.

3fill in blank

hard

Fix the error in the integration call by completing the limits for z from 0 to 1.

SciPy

result, error = tplquad(f, 0, 1, lambda x: 0, lambda x: 1, [1], lambda x, y: 1)

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A0

Blambda x: 0

Clambda x, y: 0

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using a lambda with only one argument for z limits.

Using fixed numbers instead of functions for limits.

The limits for the innermost integral (z) must be functions of x and y, here from 0 to 1.

4fill in blank

hard

Fill both blanks to complete the integration limits for y from 0 to x and z from 0 to y.

SciPy

result, error = tplquad(f, 0, 1, [1], [2], lambda x, y: 0, lambda x, y: y)

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Alambda x: 0

Blambda x: x

Clambda x, y: 0

Dlambda x, y: x

Attempts:

3 left

💡 Hint

Common Mistakes

Using lambdas with two arguments for y limits.

Swapping the lower and upper limits.

The limits for y are from 0 to x, so use lambda x: 0 and lambda x: x.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps x to the integral of f over y and z with limits y:0 to x, z:0 to y.

SciPy

results = { [1]: tplquad(f, 0, [1], lambda x: 0, lambda x: x, [2], [3])[0] for [1] in [0.1, 0.5, 1]}

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Ax

Blambda x, y: 0

Clambda x, y: y

Dy

Attempts:

3 left

💡 Hint

Common Mistakes

Using y as the dictionary key instead of x.

Incorrect lambda functions for z limits.

The dictionary keys are x values. The limits for z are from 0 to y, so use lambda x, y: 0 and lambda x, y: y.