CAB-Chp-5-2-NTs - CALCAB CHP 5-2 DEFINITE INTEGRALS Area...

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C ALC AB CHP 5-2 DEFINITE INTEGRALS Area under curves using geometry formulas
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1. Indefinite and definite integrals Anti-derivative INDEFINITE INTEGRAL
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Anti-derivative DEFINITE INTEGRAL The INTERVAL for x is [ a, b ] The LOWER BOUND of the interval starts at x = a and the UPPER BOUND ends at x = b. The interval applies to BOTH f(x) and F(x).
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2. Definite integral An application of the definite integral is AREA UNDER A CURVE f(x) over a closed interval [a, b] There are three methods to calculate the value of a definite integral (D.I.): Use special equations and geometry area formulas to get the exact value of the D.I. (today’s lesson) Use a Riemann Sums (draw rectangles or trapezoids under f(x) to estimate the value of the D.I.) (Chp 5ishC lesson, next class) Use the Fundamental Theorem of Calculus (Chp 5-3 lesson, in the near future)
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3. Definite integral, Applications Anti-derivatives undo derivatives. That means given a rate , the definite integral is a quantity
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