f m ≤ f(x) ≤ M for a ≤ x ≤ b, where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then m(b − a) ≤  b f(x) dx   a

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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If

m ≤ f(x) ≤ M

for

a ≤ x ≤ b,

where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then

m(b − a) ≤ 
b f(x) dx
 
a
 ≤ M(b − a).

Use this property to estimate the value of the integral.

2
 
0
x3 dx
 
 
(smaller value)
 
 
(larger value)
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