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GelatinousFur
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Homework Statement
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
Homework 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)
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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