Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 5 - The Integral - 5.1 Approximating and Computing Area - Exercises - Page 235: 16



Work Step by Step

Given $$ f(x)=\sqrt{6 x+2}, \quad[1,3]$$ Since $n=6$, $\Delta x= \dfrac{b-a}{n}=\dfrac{1}{3}$ and $$x_0= 1,\ x_1= 4/3,\ x_2= 5/3,\ x_3=2,\ x_4= 7/3,\ x_5= 8/3,\ x_6= 3$$ Then \begin{align*} L_{n}&=\left[f(x_0)+f(x_1)+.......+f(x_{n-1})\right]\Delta x\\ L_6&=\left[f(x_0)+f(x_1)+.......+f(x_{5})\right]\Delta x\\ &=\left[ f(1)+ f( 4/3)+ f( 5/3)+f( 2)+f( 7/3)+f( 8/3)\right]\frac{1}{3}\\ &= \left[ \sqrt{8}+\sqrt{10}+\sqrt{12}+\sqrt{14} +\sqrt{16}+\sqrt{18} \right]\frac{1}{3}\\ &=\approx 7.14 \end{align*}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.