5.2.1 Definition of integrals and the fundamental theorem Evaluating the integral from a to b of x^k dx Where k Is Any Negative Integer Other Than -1, Norman Schaumberger, 4:2, 1973, 91-93, C Some Comments on the Exceptional Case in a Basic Integral Formula, Norman Schaumberger, 5:3, 1974, 58, C, 5.3.2 Mean Value Type Theorems of Integral Calculus, C. W. Baker, 10:1, 1979, 35-37, C Using Integrals to Evaluate Voting Power, Philip D. Straffin, Jr., 10:3, 1979, 179-191, 7.2 Is Ln the Other Shoe?, Byron L. McAllister and J. Eldon Whitesitt, 12:1, 1981, 20-23, 5.3.2 Finding Bounds for Definite Integrals, W. Vance Underhill, 15:5, 1984, 426-429, C, 5.2.2 Inverse Functions, Ralph P. Boas, 16:1, 1985, 42-47, 5.3.2, 5.4.2 Average Values and Linear Functions, David E. Dobbs, 16:2, 1985, 132-135, C, 5.1.2 Using Riemann Sums in Evaluating a Familiar Limit, Frank Burk, 17:2, 1986, 170-171, C, 5.1.1, 5.3.2 The Derivatives of the Sine and Cosine Functions, Barry A. Cipra, 18:2, 1987, 139-140, C, 5.1.2 Two Simple Recursive Formulas for Summing 1^k + 2^k + ... + n^k, Michael Carchidi, 18:5, 1987, 406-409, C, 6.3 FFF #6. Cauchy's Negative Definite Integral, Ed Barbeau, 20:3, 1989, 226, F (also 20:4, 1989, 318) Riemann Integral of cos x, John H. Mathews and Haines S. Schultz, 20:3, 1989, 237, C FFF #8. A Positive Vanishing Integral, Ed Barbeau, 20:4, 1989, 317, F (also 20:5, 1989, 404) Sums and Differences vs. Integrals and Derivatives, Gilbert Strang, 21:1, 1990, 20-27 Teaching Riemann Sums Using Computer Symbolic Algebra Systems, John H. Mathews, 21:1, 1990, 51-55, C, 5.2.2 Using the Finite Difference Calculus to Sum Powers of Integers, Lee Zia, 22:4, 1991, 294-300, 5.4.1, 5.4.2 Physical Demonstrations in the Calculus Classroom, Tom Farmer and Fred Gass, 23:2, 1992, 146-148, C, 1.2, 6.1 How Should We Introduce Integration?, David M. Bressoud, 23:4, 1992, 296-298, 1.2 Riemann Sums and the Exponential Function, Sheldon P. Gordon, 25:1, 1994, 39-40, C, 5.3.2 The Integral of x^(1/2), etc., John H. Mathews, 25:2, 1994, 142-144, C The Point-Slope Formula Leads to the Fundamental Theorem of Calculus, Anthony J. Macula, 26:2, 1995, 135-139, C The Rental Car Problem, Gary D. White and Kirby Smith, 27:5, 1996, 374-378, C, 5.1.4 An Example Demonstrating the Fundamental Theorem of Calculus, Bob Palais, 29:4, 1998, 311-312, C FFF #150. Average chord length, Bernard C. Anderson, 30:4, 1999, 306-307, F Things I Have Learned at the AP Reading, Dan Kennedy, 30:5, 1999, 346-355, 0.2, 5.1.1, 5.1.2, 5.2.6, 5.4.2, 6.1 BarrowÕs Fundamental Theorem, Jack Wagner, 32:1, 2001, 58-59, C, 0.3 Integration from First Principles, Paddy Barry, 32:4, 2001, 287-289, C The Logarithm Function and Riemann Sums, Frank Burk, 32:5, 2001, 369-370, C, 5.1.1 An Average Value Inequality (Mathematics Without Words), Stephen Kaczkowski, 33:2, 2002, 166, C FFF. No antiderivative needed, Anand Kumar, 34:1, 2003, 52, F The Computation of Derivatives of Trigonometric Functions via the Fundamental Theorem of Calculus, Horst Martini and Walter Wenzel, 36:2, 2005, 154-158, C, 5.1.3, 5.3.1 If F(x) equals the integral from x to 2x of f(t) dt is Constant, Must f(t) = c/t?, Tian-Ziao He, Zachariah Sinkala, and Xiaoya Zha, 36:3, 2005, 199-204, 9.5 Self-Integrating Polynomials, Jeffrey A. Graham, 36:4, 2005, 318-320, C, 9.5 The Definition of the Integral from a to b of f(x) dx, Aaron Cinzori, 37:1, 2006, 42, C FFF #267. The integral of the derivative of any integrable function vanishes, Larry Glasser, 38:3, 2007, 219-220, F FFF #271. Two distributivity howlers, John A. Quintanilla, 38:5, 2007, 375-376, F, 5.1.4 Saddle Points and Inflection Points, Felix Martinez de la Rosa, 38:5, 2007, 380-383, C, 5.1.5 The Depletion Ratio, C. W. Groetsch, 39:1, 2008, 43-48, 5.1.1, 9.10 FFF #274. The generality of the trapezoid rule, M. A. Khan, 39:1, 2008, 50, F, 5.2.2