Mathematics 134 -- Intensive Calculus for Science 2

Quiz 1

January 25, 2006

The first regular quiz of the semester will be given during the first 15 minutes of class on Friday, January 27. It will cover the material from sections 5.3 and 5.4 on the first problem set. I will supply one of the department calculators for this quiz. The specific topics to be covered will be:

• The definite integral = limit of Riemann sums as n goes to infinity; using left- or right-hand sums to approximate the integral.
• The Fundamental Theorem of Calculus.
• First applications of definite integrals:
  1. Computing the total change of a function over some range of values of the variable, given the rate of change of that function (example: given a graph/table/formula for a velocity, compute the total distance traveled over some time interval)
  2. Computing areas between graphs and the x-axis, or between y = f(x) and y = g(x). The definite integral of f(x) gives (area above x-axis) - (area below x-axis). The area between y = f(x) and y = g(x) is the integral of f(x) - g(x) if f(x) >= g(x) on the whole interval. The questions I could ask here might involve simple graphs (say made up of parts of straight lines, circles, etc.) where areas could be found with formulas from geometry, or cases where you can find a simple antiderivative and use the Fundamental Theorem.
  3. Computing the average value of a function f(x) over a range of values of the variable.
     
     Average value = S_a^b f(x) dx/(b - a)

On the quiz, there will be two or three questions similar to problems from the problem assignments.

Good Review Problems