   Chapter 4.2, Problem 54E

Chapter
Section
Textbook Problem

# Suppose / has absolute minimum value m and absolute maximum value M. Between what two values must ∫ 0 2 f ( x )   d x lie? Which property of integrals allows you to make your conclusion?

To determine

To find:

a) Between what two values 02fxdx  must lie

b) Which Property of Integral Allows to make this conclusion

Explanation

1) Concept:

Comparison Property of Integral

i)  mfxM for axb then m(b-a)abfxdxM(b-a)

2) Calculation:

The function  f(x) has absolute minimum value m and absolute maximum value M in the interval [0,2],

Therefore, by using comparison property of Integral

If mfxM for axb then  m(b-a)abfxdxM(b-a)

Here mfxM for  0x2

Therefore, the integral of the function

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