Mathematics 134 -- Intensive Calculus for Science 2

Quiz 2

January 30, 2002

The second regular quiz of the semester will be given during the first 20 minutes of class on Friday, February. It will cover the material from sections 6.1 - 5.3 that we have discussed since the start of the week. No calculators on this quiz. The specific topics to be covered will be:

• The ``eternal gem'': The Fundamental Theorem of Calculus. If f is continuous on a <= x <= b and F is an antiderivative of f, then
  
  int_a^b f(x) dx = F(b) - F(a)
  
  Know this statement and how it comes by thinking of the integral of f as computing a total change in F.
• Antiderivatives graphically and numerically. Given a graph of f(x) for a <= x <= b, be able to generate a sketch of the graph y = F(x) where F'(x) = f(x), and F(a) = given. I will give you enough information to be able to determine values of F for at least some x -- for instance by using the Fundamental Theorem and facts about areas between the graph of f and the x-axis.
• Antiderivatives (indefinite integrals) for f defined by formulas -- know how to find antiderivatives for powers, exponentials, sin, cos, and sums and constant multiples of these.
• Using the Fundamental Theorem to compute definite integrals.
• First examples of differential equations. Finding an indefinite integral for f is the same as solving the differential equation dy/dx = f(x) for y. The arbitrary constant can be chosen to satisfy an initial condition y(a) = y₀.

On the quiz, there will be three questions similar to problems from this week's problem assignment.

Good Review Problems