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Question 10

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Saved by PBworks
on May 2, 2007 at 8:30:20 pm
 

Question 10

 

You MAY NOT use a calculator to solve this problem.

 

 

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;

 

(a)

  • unit analysis (determine what you're given in units to help determine what you're looking for)

 

 

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