To determine The length of the curve. Explanation Given: The equation of curve is y = 5 12 x 6 5 − 5 8 x 4 5 . The curve lies from x = 1 to x = 32 . Calculation: Show the equation of curve as follows. y = 5 12 x 6 5 − 5 8 x 4 5 Differentiate equation with respect to x . d y d x = d d x ( 5 12 x 6 5 − 5 8 x 4 5 ) = 5 12 d d x ( x 6 5 ) − 5 8 d d x ( x 4 5 ) = 5 12 ⋅ 6 5 x 6 5 − 1 − 5 8 ⋅ 4 5 x 4 5 − 1 = x 1 5 2 − 1 2 x 1 5 Take square on both sides. ( d y d x ) 2 = ( x 1 5 2 − 1 2 x 1 5 ) 2 = ( x 1 5 2 ) 2 + ( 1 2 x 1 5 ) 2 − 2 × x 1 5 2 × 1 2 x 1 5 = x 2 5 4 + 1 4 x 2 5 − 1 2 = 1 2 ( x 2 5 2 + 1 2 x 2 5 − 1 ) The expression to find the length of the curve y = f ( x ) on the interval [ a , b ] is as follows: L = ∫ a b 1 + ( d y d x ) 2 d x Substitute 1 2 ( x 2 5 2 + 1 2 x 2 5 − 1 ) for ( d y d x ) 2 , 1 for a , and 32 for b

14th Edition

ISBN: 9781323835029

Author: WEIR

Publisher: PEARSON C

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 6, Problem 21PE

To determine

The length of the curve.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6, Problem 20PE

Chapter 6, Problem 22PE

Students have asked these similar questions

(7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz). Ꮖ (a) (4 points) Show that V x F = 0. (b) (4 points) Find a potential f for the vector field F. (c) (4 points) Let S be a surface in R3 for which the Stokes' Theorem is valid. Use Stokes' Theorem to calculate the line integral Jos F.ds; as denotes the boundary of S. Explain your answer.

(3) (16 points) Consider z = uv, u = x+y, v=x-y. (a) (4 points) Express z in the form z = fog where g: R² R² and f: R² → R. (b) (4 points) Use the chain rule to calculate Vz = (2, 2). Show all intermediate steps otherwise no credit. (c) (4 points) Let S be the surface parametrized by T(x, y) = (x, y, ƒ (g(x, y)) (x, y) = R². Give a parametric description of the tangent plane to S at the point p = T(x, y). (d) (4 points) Calculate the second Taylor polynomial Q(x, y) (i.e. the quadratic approximation) of F = (fog) at a point (a, b). Verify that Q(x,y) F(a+x,b+y). =

(6) (8 points) Change the order of integration and evaluate (z +4ry)drdy . So S√ ² 0

Chapter 6 Solutions

MYMATHLAB ACCESS FOR CALCULUS >I< 2018

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.