Riemann Sums and Definite Integrals

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• Questions?
  • Final?
    • Cumulative but emphasizing things since 2nd exam
    • Style similar to hour exams
    • Open book, etc.
• Riemann Sums
  • Example: f′(x) = x + 1, find (a possible) f(1) by summing from 0
    
  • Section 5.3
    • Definite integral
      
    • Applications
      • Area under curve
      • NMR
        • Works by flipping atoms’ magnetic alignment and measuring energy as atoms unflip. Number of atoms with various energies is calculated from area under spikes in energy graph
        • See http://www.brynmawr.edu/chemistry/Chem/mnerzsto/The_Basics_Nuclear_Magnetic_Resonance%20_Spectroscopy_2.htm for more information
      • Average value of function
        
    • Rules
      
• The Fundamental Theorem of Calculus
  
  • Connects derivatives, antiderivatives, and definite integrals
  • Provides more practical method than Riemann sums for evaluating definite integrals
• Next
  • More on definite integrals
  • Substitution

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