Chapter 6: Q. 15 (page 510)

For each pair of definite integrals in exercise 13-18 decide which if either is larger without computing the integrals
$π \int_{0}^{2} x^{4} d x a n d π \int_{0}^{2} (x^{4} - 16) d x$

Short Answer

Expert verified

The integral $π \int_{0}^{2} x^{4} d x$ is bigger

Step by step solution

Given information

We are given two integrals

$π \int_{0}^{2} x^{4} d x a n d π \int_{0}^{2} (x^{4} - 16) d x$

Explaination

The term $x^{4} i s b i g g e r t h a n t e r m x^{4} - 16$

Hence on integrating we will get the term 16x in second integral And after substituting the limits the second term will be 16 less than that of first term. Hence the first term is bigger

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For each pair of definite integrals in exercise 13-18 decide which if either is larger without computing the integrals
$π \int_{0}^{2} x^{4} d x a n d π \int_{0}^{2} (x^{4} - 16) d x$

Short Answer

Step by step solution

Given information

Explaination

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For each pair of definite integrals in exercise 13-18 decide which if either is larger without computing the integrals π∫02x4dxandπ∫02(x4-16)dx

Short Answer

Step by step solution

Given information

Explaination

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

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Study anywhere. Anytime. Across all devices.

For each pair of definite integrals in exercise 13-18 decide which if either is larger without computing the integrals
$π \int_{0}^{2} x^{4} d x a n d π \int_{0}^{2} (x^{4} - 16) d x$