Chapter 12 Multiple choice questions

. Which of the following is not true about multiple integrals?

Single (ordinary) integrals represent the sum of a quantity along a line.

Double integrals represent the sum of a quantity over a surface.

Triple integrals represent the sum of a quantity within a volume.

As space is 3-dimensional, there is never a need to go beyond triple integrals.

. What is the Jacobian for a volume element in spherical polar coordinates (r,θ,ø) ?

1

r

r² sin(θ)

r cos(θ) sin(ø)

. What is the integral of the function F(r,θ,ø) = r² over the volume of a sphere of radius R ?

4π R⁵ / 5

2π R⁵ / 4

4π R³ / 3

2π² R³ / 3

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