   Chapter 4.2, Problem 65E

Chapter
Section
Textbook Problem

# Use properties of integrals, together with Exercises 27 and 28, to prove the inequality. ∫ 1 3 x 4 + 1   d x ≥ 26 3

To determine

To prove:

The inequality

13x4+1 dx263

Explanation

1) Concept:

i. Use comparison property of the integral:

If fxgx for  axb, then abfxdxabgxdx

ii. By exercise 28

abx2dx=b3-a33

2) Calculation:

Here,

fx=x4+1,  on    1x3

Choose gx such that fxgx. Let gx= x4

So we have

x4+1  x4

x4+1  x2

Integrate both sides of the above inequality on 1x3

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