Exam 1 will be held during the lab session on Wednesday September 27 in Room 143 Altgeld. The following topics will be covered on the exam:

Chapter 5

• Sections 5.1 & 5.2:
  • Remember that integrals are areas, so plot the function and see if the region is a geometric region for which standard formulas are known.
  • Remember that symmetries in a graph, and the area concept, can help with evaluating integrals.
  • Remember the properties of integrals on pg 306 and pg 311 and the bounds on integrals on 307 (and why they work)
  • What is the average value of a function over an interval, and why?
  • How are speed and distance, velocity and displacement related to the integral, and why?
  • What is A_f(x) and how is it connected to a specific starting value a of x?
  • How is A_f(x) changed as x increases if f is a positive function/negative function?
  • What can you say about the concavity of A_f(x)?
• Section 5.3:
  • Know the Three forms of FTC
    • A_f(x) is any anti-derivative of f
    • the integral of a derivative is the intgegrand
    • the derivative of an integral with respect to the upper limit is the integrand evaluated at the upper limit.
  • Know how to use these results to actually calculate integrals
• Sections 5.4 and 5.5:
  • Know how to apply the method of substitution
  • Know how to use tables, given that I give you some tables on an exam (I might!)
• Section 5.6:
  • Know the definitions of L_n, R_n, M_n, T_n and S_2n and how to compute them in specific examples
  • What is a general Riemann sum and how is it related to the value of an integral?
• Section 5.7: Nothing here!!

Chapter 6

• Section 6.1:
  • Know the ways in which bounds L_nand R_n are related to increasing/decreasing functions f
  • Know how bounds M_n, and T_n are connected to concave up and concave down.functions f
• Section 6.2:
  • Theorem 3 is the important result here
  • Know how to find values of K₁ and K₂ and estimate the size of n needed for a given error tolerance

Chapter 7

• Section 7.1:
  • Be prepared to compute the area between two curves using either x strips of y strips
  • Know the arc length formula, how it was formed, and how to use it in simple examples
• Section 7.2:
  • Know how to compute volumes of solids using the slice method