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1. A particle moves along the x-axis from x = 0 to x = 10, and is subject to a force field

given by F(x) = 2 + cos((pi/5) x)

The work done by the field is thus W =

integration 0 -10F(x)dx.

a) Approximate W using the left and right Riemann sums with 4 subdivisions, i.e.

using L4 and R4.

b) Explain, using a geometrical argument, why each of these actually give you the

exact value of W.

c) Confirm your value of W using the Fundamental Theorem of Calculus.

2. A circular disk of radius r is used in an evaporator and is rotated in a vertical plane. If

it is to be partially submerged in the liquid so as to maximize the exposed wetted area

of the disk, show that the center of the disk should be positioned at a height r/(sqrt(1+pi^2)) above the surface of the liquid.