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Q. 15

Expert-verified
Found in: Page 510

### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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# For each pair of definite integrals in exercise 13-18 decide which if either is larger without computing the integrals $\pi {\int }_{0}^{2}{x}^{4}dxand\pi {\int }_{0}^{2}\left({x}^{4}-16\right)dx$

The integral $\pi {\int }_{0}^{2}{x}^{4}dx$ is bigger

See the step by step solution

## Step 1: Given information

We are given two integrals

$\pi {\int }_{0}^{2}{x}^{4}dxand\pi {\int }_{0}^{2}\left({x}^{4}-16\right)dx$

## Step 2: Explaination

The term ${x}^{4}isbiggerthanterm{x}^{4}-16$

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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