ExampleFor the curve y = f(x) = x², 0 < x< 2, its length is%3Ddy1+dxdx%3D

Given curve y=f(x)=x2,0≤x≤2 The objective is to find the length of the curve.

Answered: For the curve y = f(x) = x², 0 ≤ x ≤ 2,…

Math

Calculus

For the curve y = f(x) = x², 0 ≤ x ≤ 2, its length is 2 L = 1+ dy dx dx =

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.4: Average Rate Of Change Of A Function

Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

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Question

Example
For the curve y = f(x) = x², 0 < x< 2, its length is
%3D
dy
1+
dx
dx
%3D

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but for the answer there is no denominator 5

O MAT203 VECTOR CALCULUS
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* O
MAT203 VECTOR CALCULUS
6 / 28
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Example
For the curve y = f(x) = x², 0 <x < 2, its length is
2
dy
1+
dx
VI7).
dx
4/17+ In (4 + v
0.
If we consider
s(x) = V1+ (F'(t))² dt
2.xV1+ 4x2 + ln |2x + V1+ 4x²| )
then
s(1) - 1.47894
and
s(2) - 4.64678.
Arc length
Surface area
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Arc length function
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