Fundamental Theorem - AP Calculus - Lecture Notes, Study notes of Calculus

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Calculus Section 4.4A Notes Learning Targets... 1. Evaluate a definite integral using the Fundamental Theorem of Calculus (FTC) 2. Evaluate a definite integral as a function using the Fundamental Theorem of Calculus (FTC) LT: Evaluate a definite integral using the Fundamental Theorem of Calculus (FTC) b | reoax = Fb) - F(a) e f must be continuous on [a,b] « Fis an antiderivative of f on [a,b] e The result is a constant @ Why does the C go away? e Evaluation notations... o Brackets: [F]8 = F(b) — F(a) o Bar: F|2 = F(b) — F(a) Evaluate the definite integral. SAS Mone \ [cart aan Beek -b 2 4 a 34 -2% 44 z Earl, [-eor ees] _ fp] 2 2 [oe — 6x)dx a -u 2 > Qj _ 0% Sa oy, s + -—a Soy - sGy}-0 > Single term denominator > break into ee fractions e 9 y vy 4 202 = -1 as Ce gs i ea a a =\ Sue!) ay "ae 1 1 2/3