Question 5

 

The use of a graphing calculator is NOT allowed.

 

A flat metal plate one centimeter thick is shaped like the first quadrant region under the graph of between x = 0 and x = 4. The density of the plate varies; at a distance x units from the y-axis the density is given by x² grams/cm³.

 

(a) Assume the approximate mass, ΔM, of a strip of width Δx is:

ΔM = (volume)(density)

Write a left-hand Riemann sum with 4 terms that approximates the total mass of the metal plate.

 

(b) Write a definite integral that gives the exact value of the total mass of the plate.

 

(c) Determine the total mass of the plate.

 

 

Solution