Line & Surface Integrals

The del operator is called as

• a) Gradient

• b) Curl

• c) Divergence

• d) Vector differential operator

The Gauss divergence theorem converts

• a) line to surface integral

• b) line to volume integral

• c) surface to line integral

• d) surface to volume integral

If the orientation of curve C is in clockwise orientation, thus the normal vector of the surface S is in positive orientation.

• True.

• False

• 8

What do line integrals calculate?

• The minimum value of a vector field

• The average of a vector field over a surface

• The sum of a function along a curve or path

• The maximum value of a scalar field

What do surface integrals calculate?

• The maximum value of a scalar field

• The total value over a surface

• The minimum value of a vector field

• The average value of a vector field

Which theorem relates the line integral of a vector field around a closed curve to the surface integral of the curl of the vector field?

• Divergence Theorem

• Pythagorean Theorem

• Green's Theorem

• Stokes' Theorem

Green's theorem connects

• line integral and double integral

• line integral and Surface integral

• double integral and Surface integral

• surface integral and volume integral