   Chapter 16, Problem 2RE

Chapter
Section
Textbook Problem

Evaluate the line integral.2. ∫C x ds, C is the arc of the parabola y = x2 from (0, 0) to (1, 1)

To determine

To Evaluate: The line integral Cxds for an arc of the parabola y=x2 from (0,0) to (1,1) .

Explanation

Given data:

The parametric equations of curve and its limits are given as follows.

x=x , y=x2 from (0,0) to (1,1) .

Formula used:

Write the expression to evaluate the line integral for a function f(x,y) along the curve C .

Cf(x,y)ds=abf(x(t),y(t))(dxdt)2+(dydt)2dt (1)

Here,

a is the lower limit of the curve C and

b is the upper limit of the curve C .

Write the required differential and integration formulae to evaluate the given integral.

ddxxn=nxn1[f(x)]ndx=[f(x)]n+1n+1(uv)dx=uvdxu(vdx)dx

Modify equation (1) as follows.

Cf(x,y)ds=abf(x,y)(dxdx)2+(dydx)2dx

Substitute x for f(x,y) , x for x , x2 for y , 0 for a , and 1 for b ,

Cxds=01x(ddx(x))2+(

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