![]() Note however, the process used here is identical to that for when the answer is one of the standard angles. ![]() (displacement)Įx: Given Find the displacement and total distance traveled from time 1 to time 6. Solving Trig Equations with Calculators, Part I In this section we will discuss solving trig equations when the answer will (generally) require the use of a calculator ( i.e. Part 1 of the Fundamental Theorem of Calculus (FTC) states that given F ( x ) a x f ( t ) d. The integral of a rate of change is the total change from a to b. The Fundamental Theorem of Calculus and the Chain Rule. 1 The Fundamental Theorem of Calculus Part 1 & 2 2 Let, where g is graphed below 3 If what is g(1) 4 Improper Integrals (Well evaluate them in chapt. ![]() Using the given graph, estimate Why are your answers in parts (a) and (b) different? ( ) Helps us to more easily evaluate Definite Integrals in the same way we calculate the Indefinite!ġ2 In-class Assignment Estimate (by counting the squares) the total area between f(x) and the x-axis. If f is continuous on, then : Where F is any antiderivative of f. Solution for 7-18 Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. If f is continuous on, then the function defined by is continuous on and differentiable on (a, b) andĨ Fundamental Theorem of Calculus (Part 1)ĩ Fundamental Theorem of Calculus (Part 2) Interval is infinite (easiest to identify) Function “Blows” up! (down)ĥ Which of the following integrals are improper?Ħ Fundamental Theorem of Calculus (Part 1) (Chain Rule) Fundamental Theorem of Calculus, Part 1 If f (x) f ( x) is continuous over an interval a,b, a, b, and the function F (x) F ( x) is defined by F (x) x a f(t)dt, F ( x) a x f ( t) d t, then F (x) f (x) F ( x) f ( x) over a,b. The second part of the fundamental theorem of calculus provides an efficient way to evaluate definite integrals, rather than needing to approximate area using. 7)Īn integral having at least one nonfinite limit or an integrand that becomes infinite between the limits of integration. Fundamental Theorem of Calculus Part 1 If f ( x ) is continuous over an interval a, b, and the function F ( x ) is defined by F ( x ) a x f ( t ) d t. Part 1 establishes the relationship between differentiation and integration. Presentation on theme: "The Fundamental Theorem of Calculus Part 1 & 2"- Presentation transcript:ġ The Fundamental Theorem of Calculus Part 1 & 2įind: On what interval(s) is f increasing? What are the Max/Min values of f on ?Ĥ Improper Integrals (We’ll evaluate them in chapt.
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