Answer :
Final answer:
Reparametrizing a curve alters the parameter of the function representing the curve. In this example, we use the parameters t+4, t-4, and t^2 - 4t to create equivalent functions that simplify computation of integrals,
Explanation:
The process of reparametrizing a curve involves changing the parameter of the function that represents the curve. Given the point (-4, 1, -4), and the instructions to reparametrize the curve using t+4, t-4, and t^2 - 4t, we will alter the curve's parameter.
Reparametrizing using t+4 gives us the curve (t+4)^2 which when evaluated at t=-4 gives us the original point (-4 ,1, -4). Similarly, Reparametrizing using t-4 gives us the curve (t-4)^2 which when evaluated at t=-4 gives us the original point. Lastly, reparametrizing the curve using the equation t^2 - 4t involves substituting the new parameter which will give us a new curve but keeping the same point.
Reparametrizing is used in calculus, specifically in integrals, to create equivalent functions that simplify the computation of complex integrals.
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