Find Equation of Curve: y=f(x), f'(x)=(x-1)^2, (4,3)

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The discussion focuses on finding the equation of a curve defined by the derivative f'(x) = (x-1)^2, which passes through the point (4,3). To derive the equation, participants suggest performing a u-substitution with u = x - 1, leading to the integral of f'(x). After integrating and applying the initial condition, the constant C can be determined to finalize the equation of the curve.

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a curve y=f(x) passes through the point (4,3)
if f'(x) = (x-1)^2 find the equation of the curve.
 
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That's pretty easy to integrate. Just perform a u-substitution with u=x-1 and du=dx. Then put in your initial conditions to solve for C.
 
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