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

Evaluate the following line integral on the indicated curve C

[tex]\int(y^2-x^2)ds[/tex]

C: x = 3t(1+t), y=t^3 ; 0 <= t <= 2

2. Relevant equations

ds = [tex]\sqrt{(f'(t))^2+(g'(t))^2}dt[/tex]

3. The attempt at a solution

dx/dt = 3+6t

dy/dt = 3t^2

ds = [tex]\sqrt{(3+6t)^2+(3t^2)^2}[/tex]dt

ds = 3*[tex]\sqrt{t^4+4t^2+4t+1}[/tex]dt

y^2 = t^6

x^2 = (3t+3t^2)^2 = 9t^2+18t^3+9t^4

[tex]\int(y^2-x^2)ds = 3\int(t^6-9t^2-18t^3-9t^4)\sqrt{t^4+4t^2+4t+1}dt[/tex]

From here I don't know how to solve the integral, and it looks way more complicated than what we have done so far in class. Maybe I am doing something wrong? Or there is a trick involved here? Any help would be greatly appreciated. Thanks.

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# Line integral problem

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