Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 5 - Section 5.2 - The Definite Integral - 5.2 Exercises: 18

Answer

$\int_{2}^{5}x\sqrt{1+x^3}dx$

Work Step by Step

We know the following $\int_{a}^{b}f(x)dx=\lim\limits_{n \to \infty}\sum\limits_{n=1}^{\infty}f(x_i)\Delta x $ $\Delta x= \frac{b-a}{n}$ $x_i= a+i\Delta x$ In our problem we can see that $f(x)=x\sqrt{1+x^3}$ We are given that the interval of integration is from 2 to 5 therefore these will be our limits of integration Therefore $\lim\limits_{n \to \infty}\sum\limits_{n=1}^{\infty}x_i\sqrt{1+x_i^3}\Delta x=\int_{2}^{5}x\sqrt{1+x^3}dx$
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