5.3 Fundamental Theorem of Calculus

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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online