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Numerade Educator

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Problem 2 Easy Difficulty

Find the most general antiderivative of the function.
(Check your answers by differentiation.)

$ f(x) = x^2 - 3x + 2 $

Answer

$F(x)=\frac{x^{3}}{3}-\frac{3 x^{2}}{2}+2 x+C$

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Video Transcript

So here we're trying to calculate the general anti derivative of the given function function that we have is F of X equals x squared -3. Act plus two. So when you take the anti derivative of this we have X squared. The anti derivative of that. We add one to the power so it's X cubed. Okay, divided by three minus three Acts. So we add one to the power. So that's the me minus three X squared. Then we have to divide that by two And then we have plus two x. Because the constant values we just multiply by X. And then we have the general constant plus C. Then what we end up but up happening is if we take F prime of X, we see that regardless of what psi is, we end up getting the same exact value of the F. Time function as we do this function right here. So we've done it correctly.