Suppose f has absolute minimum value m and absolute maximum value M. Between what two values must  3 f(x) dx   0  lie?         (smaller value)         (larger value) Which property of integrals allows you to make your conclusion?   c f(x) dx   a +  b f(x) dx   c =  b f(x) dx   a    a f(x) dx   a = 0      If m ≤ f(x) ≤ M for a ≤ x ≤ b, then m(b − a) ≤

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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Suppose f has absolute minimum value m and absolute maximum value M. Between what two values must 

3 f(x) dx
 
0

 lie?

 
 
 
  (smaller value)
 
 
 
  (larger value)


Which property of integrals allows you to make your conclusion?

 
c f(x) dx
 
a
 + 
b f(x) dx
 
c
 = 
b f(x) dx
 
a
 
 
a f(x) dx
 
a
 = 0
    
If m ≤ f(x) ≤ M for a ≤ x ≤ b, then m(b − a) ≤ 
b f(x) dx
 
a
 ≤ M(b − a).
If f(x) ≥ 0 for a ≤ x ≤ b, then 
b f(x) dx
 
a
 ≥ 0.
 
b f(x) dx
 
a
 = −
a f(x) dx
 
b
 
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