Fundamental Theorem Of Calculus Part 2 Walkthrough Fundamental Theorem of Calculus Part 1 The Organic Chemistry Tutor 980K views 5 years ago This calculus video tutorial provides a basic introduction into the fundamental theorem of calculus
Use the Fundamental Theorem of Calculus Part 2 to evaluate definite integrals Explain the relationship between differentiation and integration In the previous two sections we looked at the definite integral and its relationship to the area under the curve of a function The Fundamental Theorem of Calculus Part 2 FTC 2 relates a definite integral of a function to the net change in its antiderivative Fundamental Theorem of Calculus Part 2 If f is continuous on a b and F x f x then a b f x d x F b F a
Fundamental Theorem Of Calculus Part 2 Walkthrough
Fundamental Theorem Of Calculus Part 2 Walkthrough
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PPT THE FUNDAMENTAL THEOREM OF CALCULUS PowerPoint Presentation Free Download ID 6886787
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5 3 5 Use the Fundamental Theorem of Calculus Part 2 to evaluate definite integrals 5 3 6 Explain the relationship between differentiation and integration In the previous two sections we looked at the definite integral and its relationship to the area under the curve of a function Courses on Khan Academy are always 100 free Start practicing and saving your progress now https www khanacademy math ap calculus ab ab integration
Access the PDF of the notes from this video here http clairegibbons s FTC part2 pdfThis video is explains how we evaluate definite integrals using the The Fundamental Theorem of Calculus Part 2 is perhaps the most important theorem in calculus After tireless efforts by mathematicians for approximately 500 years new techniques emerged that provided scientists with the necessary tools to explain many phenomena Using calculus astronomers could finally determine distances in space and map
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The amazing aspect of part 2 is that this function has a derivative equal to the function we are nding the area under namely f A simple way to remember part 2 and in particular equation 1 is that the derivative and integral sign cancel out See the Fundamental Theorem of Calculus Part 1 The Fundamental Theorem of Calculus Part 2 is a formula for evaluating a definite integral in terms of an antiderivative of its integrand The total area under a curve can be found using this formula See the Fundamental Theorem of Calculus Part 2
The Second Fundamental Theorem of Calculus is the formal more general statement of the preceding fact if f is a continuous function and c is any constant then A x x cf t dt is the unique antiderivative of f that satisfies A c 0 d dx x cf t dt f x The fundamental theorem of calculus is very important in calculus you might even say it s fundamental It connects derivatives and integrals in two equivalent ways I d d x a x f t d t f x I I a b f x d x F b F a The first part says that if you define a function as the definite integral of another function
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Fundamental Theorem Of Calculus Part 2 Walkthrough - The Fundamental Theorem of Calculus tells us that the derivative of the definite integral from to of is provided that is continuous Rather it is the first fundamental theorem or the first part as some sources prefer In fact if you don t believe me look at the video below in the AP BC
