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Chapter 1: Limits and Their Properties
Antiderivatives by substitution of variables (including change of limits for definite integrals). E. Applications of Antidifferentiation. Finding specific antiderivatives using initial conditions, including applications to motion along a line. Solving separable differential equations and using them in modeling. In particular, studying the ...
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[DOCX File]I. Functions, Graphs, and Limits
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Evaluate limits of functions. Differentiate algebraic and transcendental functions. ... inflection points, asymptotes, holes, etc. Find anti-derivatives of functions and evaluate definite integrals using the definition of the integral and the Fundamental Theorem of Calculus. Evaluate definite and indefinite integrals using substitution. Book ...
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[DOC File]Section 1 - Radford
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Evaluate definite integrals as limits of Riemann Sums . Introduction. In the Lesson The Area Problem we defined the area under a curve in terms of a limit of sums. where . and were examples of Riemann Sums. In general, Riemann Sums are of form where each is the value we use to find the length of the rectangle in the sub-interval.
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[DOC File]Calculus II
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• Infinite limits • Using limits to find the asymptotes of a function . Chapter 2: Differentiation (2-2.5 weeks, 1 test, daily quizzes) ... • Use of the First Fundamental Theorem to evaluate definite integrals • Use of substitution of variables to evaluate definite integrals
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[DOCX File]Louisiana State University
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The numbers a and b are said to be the limits of integration. For our problems, a < b. Definite Integrals are evaluated using The Fundamental Theorem of Calculus. Fundamental Theorem of Calculus. Let be a continuous function for and be an antiderivative of . Then. Example 1: Evaluate . Solution: Example 2: Evaluate .
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4.7: Definite integrals by substitution. - Mathematics ...
Topic 5: Evaluating Definite Integrals Using Limits If f is integrable on [a,b] , then a b f x dx= lim ∆→0 ∑ k=1 n f x k * ∆ x k for any partition of [a,b] and any point x k * . To simplify the calculations, we will use equally spaced grid points and a right Riemann sum to evaluate definite integrals using limits.
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[DOCX File]172 Calculus 2
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Evaluate definite integrals using Riemann Sums and the Fundamental Theorem of Calculus. 8. Utilize Calculus techniques to solve application problems. Topical Outline . REQUIRED TOPICAL OUTLINEI. Limits using appropriate analytical, numerical or graphical techniques. a. Limits computation. b. Properties of limits. c. Limits at infinity. d ...
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Part 2: - Pikes Peak Community College | Colorado Springs
Use what you know about indefinite integrals to confirm that Carla’s calculator is correct. (b) Evaluate the definite integral without a calculator. The final answer involves square roots. (c) Write the name of the theorem you used to evaluate the integral in (b). _____ 7. …
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[DOC File]Indefinite Integrals Calculus
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The definite integral is an improper integral because a discontinuity in the function occurs within the limits of integration. To correctly evaluate the improper integral, we need to express the original integral as the sum of two integrals so that the value of x at which a discontinuity occurs is either an upper or lower limit of integration:
evaluate integral using limit definition

Evaluate definite integrals using limits