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Find the length of curve by integration, quadratic equation

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Consider that two particles are traveling the paths of the following functions:

f(x)=3/4x^2-x+1
g(x)=-x^2+2x+3

If each particle is to begin at one point of intersection at the same time and travel to the other point of intersection (at the same velocities), then which particle would arrive first? WHY?

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Solution Summary

In this case, I presented some detailed explanation how the length of curve was solved by integration and quadratic equation.

Solution Preview

First find the interaction point:

f(x)=g(x), 3/4x^2-x+1 =-x^2+2x+3 , we ...

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