The document explains how to calculate the mass of a piece of metal using Riemann sums. It defines volume as length times width times height, with width set to 1 cm. Density is defined as the square of x, where x is the average density. Mass is calculated as volume times density. A left-hand Riemann sum is used to calculate the mass by dividing the interval from 0 to 4 into 4 equal subdivisions and summing the areas of the rectangles.

1. Question # 2
Answer explained by: DinoP

2. Here is a 3D representation
of what is wanted from this
question.

3. Volume is defined by the function
f(x) = l * w * h, where:
(w) width = 1 cm
Density is defined by the function
(h) height = g(x) = x2
*As height is
dependent on x* x2 = is the average density of the piece of
metal.
(l) length = x2 ­ x1

4. Mass = (Volume)(Density)
Volume = f(x) =
Density = g(x) =
Mass = f(x) * g(x)
Mass =

5. Using the Left Hand Riemann sum we recieve: