5.3 Fundamental Theorem of Calculus

5.3 Fundamental Theorem of Calculus - MAC2233(3.4 North FIU...

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MAC2233 (3.4) FIU, MDC- North Area Under a Curve:   If  f(x)  is continuous and  f(x) ≥ 0  on the interval  a ≤ x ≤ b , then the region under the curve  y =  f(x)  over the interval  a ≤ x ≤ b  has area  ( 29 ( 29 ( 29 n n A f x f x f x x 1 2 lim ... →∞ = + + +  where  x j  is the left endpoint  of the  jth  subinterval if the interval  a ≤ x ≤ b  is divided into  n  equal parts, each of length  b a x n - ∆ = .  This area is  more easily computed using the  fundamental theorem of calculus:   If  f(x)  is on the interval  a ≤ x ≤ b , then  ( 29 ( 29 ( 29 ( 29 b b a a f x dx F x F b F a = = - .  Rules for Definite Integrals:  If  f  and  g  are any continuous function on  a ≤  x ≤ b , then [1]  Constant Multiple Rule:   b b a a kf x k f x ( ) ( ) =  for constant 
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5.3 Fundamental Theorem of Calculus - MAC2233(3.4 North FIU...

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