Let be a quadratic polynomial such that

Since is a quadratic polynomial we can write,

Then, gives us and gives us

Finally, evaluating the integral we have

Thus, we have

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Stumbling Robot

A Fraction of a Dot
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Find a degree 2 polynomial to satisfy an integral equation

Let be a quadratic polynomial such that

Since is a quadratic polynomial we can write,

Then, gives us and gives us

Finally, evaluating the integral we have

Thus, we have