lect116_26rev_f11

lect116_26rev_f11 - 5.4 1, 3, 5, 7, 11, 13, 14, 25, 27, 29,...

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Friday, November 11 Lecture 26 : Antiderivatives (Refers to Section 5.4, 5.5 in your text) Students who have mastered the content of this lecture know about : The Fundamental theorem of calculus, the general antiderivative of a function, the indefinite integral of a function. Students who have practiced the techniques presented in this lecture will be able to : Compute the definite integral of a simple function by first finding its antiderivative, find the area of a region bounded by two curves over an interval. 26.1 Properties of indefinite integrals. Indefinite integrals have properties which are similar to the ones of definite integral . We will list them here and prove a few of these so that students can see how the proofs do not involve limits of Riemann sums. 26.2 A few indefinite integrals determined directly from the definition.
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26.3 Examples. Recommended exercises associated to this lecture and the previous lecture : §
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Unformatted text preview: 5.4 1, 3, 5, 7, 11, 13, 14, 25, 27, 29, 31, 41, 53, 62. 5.5 1-14, 41 26.4 Proposition Suppose f ( x ) g ( x ) over the interval [ a , b ]. Then the area of the region bounded by the curves of f and g over [ a , b ] is given by the number obtained from Proof is given in class. 26.4.1 Example Find the area of the region bounded by f ( x ) = sin x and g ( x ) = cos x over the interval [0, ] 26.5 Various examples on the FTC. Note : In physics you may have used a given formula to compute the above value. Verify that the same answer is obtained whichever way you choose to solve the problem. 26.6 Example Compute the derivative (with respect to x ) of the given function g ( x ) in two ways: The first by direct integration followed by differentiation, the second by invoking part I of the FTC. Using part II of the FTC: Using part I of the FTC:...
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This note was uploaded on 12/28/2011 for the course MATH 116 taught by Professor Robertandre during the Spring '11 term at Waterloo.

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lect116_26rev_f11 - 5.4 1, 3, 5, 7, 11, 13, 14, 25, 27, 29,...

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