Double integral (dblquad) in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

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

SciPy

from scipy.integrate import [1]

result, error = dblquad(lambda x, y: x*y, 0, 1, lambda x: 0, lambda x: 1)
print(result)

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

Adblquad

Bquad

Ctrapz

Dsimps

Attempts:

3 left

💡 Hint

Common Mistakes

Importing 'quad' instead of 'dblquad'.

Using 'trapz' or 'simps' which are for numerical integration but not double integrals.

The dblquad function is used for double integrals in scipy.integrate.

2fill in blank

medium

Complete the code to set the limits of integration for y as functions of x.

SciPy

from scipy.integrate import dblquad

result, error = dblquad(lambda x, y: x + y, 0, 2, [1], lambda x: 3)
print(result)

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Alambda x: 0

Blambda y: 3

Clambda x: 2

Dlambda y: 0

Attempts:

3 left

💡 Hint

Common Mistakes

Using lambda with y instead of x for limits.

Using a constant instead of a function for limits.

The lower limit for y must be a function of x, so lambda x: 0 is correct.

3fill in blank

hard

Fix the error in the order of variables in the integrand function for dblquad.

SciPy

from scipy.integrate import dblquad

result, error = dblquad(lambda [1], 0, 1, lambda x: 0, lambda x: 1)
print(result)

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

Ax, y: y*x

By, x: x*y

Cx, y: x*y

Dy, x: y*x

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping the order of variables in the lambda function.

Using y first instead of x.

The integrand function for dblquad must have the order lambda x, y: ....

4fill in blank

hard

Fill both blanks to correctly compute the double integral of f(x,y) = x^2 + y^2 over x in [0,1] and y in [0,2].

SciPy

from scipy.integrate import dblquad

result, error = dblquad(lambda [1]: x**2 + y**2, 0, 2, [2], lambda y: 1)
print(result)

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

Ax, y

By, x

Clambda y: 0

Dlambda x: 0

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping x and y in the lambda function.

Using a constant instead of a function for limits.

The integrand must be lambda x, y and the lower limit for x is lambda y: 0.

5fill in blank

hard

Fill all three blanks to compute the double integral of f(x,y) = x*y over x in [0, y] and y in [0, 1].

SciPy

from scipy.integrate import dblquad

result, error = dblquad(lambda [1]: x*y, 0, 1, [2], [3])
print(result)

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

Ax, y

Blambda y: 0

Clambda y: y

Dlambda x: 1

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up the order of variables in the lambda function.

Using incorrect limits for the inner integral.

The integrand is lambda x, y, the lower limit for x is lambda y: 0, and the upper limit for x is lambda y: y.