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Numerade Educator

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Problem 4 Medium Difficulty

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

$ f(x) = 6x^5 - 8x^4 - 9x^2 $

Answer

$F(x)=4 x^{\wedge} 3+4 x^{\wedge} 2+c$

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Video Transcript

this problem our goal is to take the general anti derivative of the function. The function given to us is ethel Becks equals six X. to the 5th. Mhm. Mhm. Right. It's eight X to the 4th. It's -9 x squid. And this is what we end up getting as a result. Then um we want to take the anti derivative, this big F of X. We take the anti derivative of each individual portion six X to the fifth. That's going to become extra the six. So six X To the 6th divided by six. That's just X to the 6th. And we have minus, we act to the four or eight X to the fifth because we raised the power and then we divide that by five and then we have minus nine X. Cubed. We raise that over three. I was just going to give us three X. Cute. And lastly we have to add the general constant. And this will be our final anti derivative.