Double Integrals Quiz

A double integral ∬R f(x, y) dx dy represents:

• Volume under the surface over region R

• Area of region R

• Length of curve

• Surface area

Double integrals are generally used to compute:

• Line integrals

• Area under curve

• Volume under surfaces

• Derivatives of a function

Which of the following is a correct notation for a double integral?

• ∫∫ f(x, y) dx

• ∫ f(x, y) dx dy

• ∫∫ f(x, y) dx dy

• ∂∫ f(x, y) dx dy

In double integrals, the region of integration is called:

• Curve

• Plane

• Domain

• Line

To evaluate ∬R f(x, y) dx dy, R must be:

• An interval

• A line segment

• A region in the xy-plane

• A point

Which order of integration is commonly used in rectangular regions?

• dy first, then dx

• dx first, then dy

• Both A and B depending on limits

• Always dy first

When is change of order of integration necessary?

• Always

• When the region is non-rectangular

• To simplify evaluation

• B and C

Polar coordinates are useful when the region is:

• Rectangular

• Circular

• Triangular

• Trapezoidal

In polar coordinates, x and y are represented as:

• x = r cosθ, y = r sinθ

• x = r sinθ, y = r cosθ

• x = θ cos r, y = θ sin r

• x = rθ, y = θr

The double integral in polar coordinates includes an extra factor:

• sin θ

• cos θ

• r

• θ