(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate the line integral [tex]\[ \int_c yz\,ds.\][/tex]

where C is a parabola with z=y^2 , x=1 for 0<=y<=2

2. Relevant equations

A hint was given by the teacher to substitute p=t^2 , dp=(2t)dt and use integration by parts.

I also know from other line integrals with respect to arc length that:

ds=sqrt((dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2)

3. The attempt at a solution

I think that from the information given, the beginning and end points are (1,0,0) to (1,2,4).

My first guess is:

x(t) = t

y(t) = 2t

z(t) = t^2

This will be when t goes from 0 to 2.

So after I have parameterized the curve, I would substitute the functions of t back into the integral to get:

int((2t)^3*sqrt(1^2+2^2+(2t)^2),t,0,2)

=8*int(t^3*sqrt(4t^2+5),t,0,2)

=12032/3

This doesn't look right to me though. Any help would be appreciated!

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# Evaluation of a (parabolic) line integral with respect to arc length

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