Let be the curve parameterised by , for 1.

Let , where .   

Then the value of line integral

is...

Let be a scalar field and be a curve defined by the vector valued function , . Then the line integral of  along is given by: 

where

Consider the Example 1.4.18 from the lecture notes. The radius of the sphere is halved to R/2 units.

Find the volume of the small sphere:

a)

b)

c)

Based on your current understanding of each topic, which worksheet question(s) would you most like the workshop leader to demonstrate?

There is no wrong answer to this question. The collective responses will inform the discussion in the workshops.

Consider the Example 1.4.18 from the lecture notes. The radius of the sphere is halved to R/2 units.

Find the volume of the small sphere:

a)

b)

c)

Let be the solid quarter sphere with centre and radius 1 in which and .

The triple integral written in spherical coordinates is

(a):

(b):

(c):

(d):

(e):

Let be a solid region, with density , given in cylindrical coordinates.   Then the mass of  is given by...