Computing the line integral of the scalar function over the curve

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To compute the line integral of the scalar function f(x,y) = √(1 + 9xy) over the curve defined by y = x^3 from x = 0 to x = 1, parameterization is essential. The suggested parameterization is x = t and y = t^3, leading to the curve represented as R(t) = ⟨t, t^3⟩ for 0 ≤ t ≤ 1. This approach allows for the substitution of the parameterized variables into the function. The integral can then be evaluated using the appropriate limits and the derived expressions. Understanding the parameterization is key to solving the problem effectively.
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Homework Statement


f(x,y) = \sqrt{1+9xy}, y = x^{3} for 0≤x≤1


Homework Equations





The Attempt at a Solution


I don't even know how to start this problem. I thought about c(t) since that's all I have been doing, but there isn't even c(t). I only recognize domain. Can anyone help me please?
 
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Start with parameterization x = t, y = t3 so your curve is given by
\vec R(t) = \langle t, t^3\rangle,\, 0\le t\le 1
 

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