The derivative of an integral
[DOC File]Integration
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The Indefinite Integral. The Definite Integral. Application Problems Definition. Integration is a process that recovers the original function from its derivative within the boundary of not knowing the constant term. Denoted: F(x) = “F(x)” is called the “anti-derivative”. Taking a definite integral is …
[DOC File]Lecture Notes on Calculus
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The Derivative Algorithm. The derivative algorithm is a formulation that answers the question, what is the instantaneous rate of change of a dependent variable –y- with respect to the independent variable x . The derivative is denoted by dy/dx is an analytic function say g(x) ,equal to the limit of the slope ,(∆y/∆x) as ∆x tends to zero.
[DOC File]AP Calculus Free-Response Questions
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c. Set up but do not evaluate an integral representing the volume of the solid generated when R is. rotated about the y-axis. Express the integrand as a function of a single variable. 49. Given a function f with the following properties: (i) f(x + h) = eh f(x) + ex f(h) for all real numbers x and h. (ii) f(x) has a derivative for all real ...
[DOC File]MATH 140: Calculus – D
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TEXT: Math 140 comprises Chapters 2-5 of the calculus book by Robert Ellis and Denny Gulick (any 6th edition 2003 or later). Chapter 2 concerns limits; Chapters 3 and 4 focus on the derivative and applications of the derivative; Chapter 5 introduces the integral. The text is written to be read by you.
[DOC File]What Is Calculus
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This connection between the integral and the derivative is known as the Fundamental Theorem of the Calculus. Stated in symbols:The function F(x), which is equal to the integral of f(x), is sometimes called an antiderivative of f(x), while the process of finding F(x) from f(x) is called integration or antidifferentiation.
[DOC File]AP Physics C: Mechanics
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Application activities include formalization of derivative and integral concepts by establishing relationships between x, v, and a with respect to t. Lab: Determination of a for a freely falling object. Validate a=10m/s/s regardless of mass and derivative/integral concepts for freely falling objects.
[DOCX File]Calculus I
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Worksheet HW 3.3: “Increasing and Decreasing Functions & The First Derivative Test” 1-13 all
[DOC File]Indefinite Integrals Calculus
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Use the Fundamental Theorem to find the derivative of the following function: Solution: In this example, the integral is more difficult to evaluate. The Fundamental Theorem enables us to find the answer routinely. Lesson Summary. 1. We used the Fundamental Theorem of Calculus to evaluate definite integrals. Fundamental Theorem of Calculus
[DOC File]Relationship between the Derivative and the Integral and ...
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Relationship between the Derivative and the Integral and the Graphs. Mini-Project -- 30 points. Due by 6:41 a.m. on Monday, 3/13/17. This is the second of 4 problems designed to help you solidify your understanding of major calculus topics.
[DOC File]Relationship between the Derivative and the Integral ...
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2. In your paper, you discussed various ways that the derivative and integral could be used in a variety of contexts. Please discuss the following problem: Water is draining out of a tank at a variable rate as given by the graph and chart below. t R(t) gal/min 0 0 5 5 10 20 20 30 30 15 35 0
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