The Fundamental Theorem of Calculus (Part 2) Suppose that f is continuous on -a, Answers to Sample Problems 1 a) # b) 8412fi421 c) $ ) 2 a) x
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20 mar 2008 · we discuss a definition of the natural logarithm as an integral Part I of the Fundamental Theorem of Calculus that we discussed in
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37 2 2 Example Find ? 5 1 3x2 dx Solution We use part (ii) of the fundamental theorem of calculus with f(x)=3x2 An antiderivative of f is F(x) = x3,
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Recall the Take-home Message we mentioned earlier Example 1 5 5 points out that even though the definite integral 'solves' the area problem, we must still
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16 avr 2014 · 2 Use of the Fundamental Theorem of Calculus (F T C ) Solution: 1) Areas: ? 3 0 (2 ? x)dx Example: Evaluate using the F T C
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we can understand why the integral gives the answers to particular problems Example 5: Find a formula for A(z) = / (4t + 2) dt, that is, evaluate the
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5 4 Fundamental Theorem of Calculus Part II: Suppose that f(x) is a continuous aF (x) dx = F(b) ? F(a) Example: ? 2 01+2x ? x2 dx = [x + x2 ?
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The definite integral is a number Exercises: (problems #1–3 focus on part 1 of the FTC, while the remaining problems use part 2) 1
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29 jan 2015 · 2 dt Solution We don't know how to evaluate the integral ? We're almost ready for examples using part 2 of the Fundamental Theorem
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Solution 5 4 Indefinite Integrals and the Net Change Theorem In Section 5 3 we used the FTC, part 2, to evaluate the definite integral of a function
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