Due date: Sunday 2/8, 11:59pm
Arc length
01
03
Link to originalArc length - tricky integration
Find the arc length of the curve
for . (Hint: the integral can be done using either: (i)
-sub then trig sub, or (ii) ‘rationalization’ then partial fractions.)
Solution
Surface areas of revolutions - thin bands
02
02
Link to originalSurface area: cone
A cone may be described as the surface of revolution of a ray emanating from the origin, revolved around the
-axis. Let
for some . Find the surface area of the cone given by revolving the graph of around the -axis over . Can you also calculate this area using geometry? And verify the two methods give the same formula? (Hint: ‘unroll’ the cone into a sector.)
Solution
03
03
Link to originalSurface area: parabolic reflector
A parabolic reflector is given by rotating the curve
around the -axis for . What is the surface area of this reflector?
Solution