lect116_25rev_f11

lect116_25rev_f11 - Thursday, November 10 Lecture 25 :...

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Thursday, November 10 Lecture 25 : Fundamental theorem of calculus. (Refers to Section 5.4, 5.5 in your text) Students who have mastered the content of this lecture know : The Fundamental theorem of calculus, the definition of “antiderivative” and the general antiderivative of a function f(x), the net change of a function over an interval [a, b]. Students who have practiced the techniques presented in this lecture will be able to : State both parts of the FTC and apply the FTC directly to integrals, compute the definite of integral of a simple function by first finding an antiderivative of the function, compute the net change of a function over an interval. The Fundamental theorem of calculus is a theorem which links “differential” calculus to “integral” calculus. It shows that differentiation (finding slopes of tangent lines to a curve) and integration (computing areas of regions), two apparently unrelated processes are actually inverses of each other. Note: It is important to note that the FTC is actually two statements. We often refer to them as “Part I and Part II of the FTC”. But different authors may choose to order them differently. So in a different text look carefully to determine how the author prefers to order them. 25.1 The Fundamental theorem of calculus (FTC) – Let f be continuous on the interval [ a , b ] and g ( x ) be the function defined as Then: 1) The function g ( x ) is continuous on [ a , b ] and differentiable on ( a , b ) and for any x strictly between a and b , g ( x ) = f ( x ).
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lect116_25rev_f11 - Thursday, November 10 Lecture 25 :...

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