determine-the-value-of-a-that-makes-fx-an-antiderivative-of-fx-fx3-x2-fxa-x3-3

Question

Determine the value of a that makes $F(x)$ an antiderivative of $f(x)$
$$f(x)=3 x^{2}, F(x)=a x^{3}$$

Tyler Moulton · Accepted Answer

we want to find the constant A. Such that f of x equals a execute is an anti derivative of lower case F of x equals three X square. This question is challenging our knowledge of anti differentiation as a precursor to integration. So we need to understand this topic, remember that the anti derivative is an inverse derivative function. Thus we need to know DDX or rather derivative rules to understand anti directly rules. So I was the powerful product rule and chain rule on the right. In this particular problem we see that for three X squared converting to its anti derivative, we need to use the inverse power rule so it&#x27;s rid of extra is 80 x minus one. The anti rid of of extra. I should be one over A actually a plus one. Thus we can perceive the entire delivery with this in mind. Thus we have F one equals three times one third X. Q. Or execute. Thus we solve for a such that are F one is equal to R. F, so for X equals F one we have a equals one

Linh Vu · Answer

in this question. We&#x27;re leaving the function f X go you 68 about three thanks. And we need to find the untidy reviewing a function and accounts down six to stay the same for this one. We know that they were trying to able three x River Day. We get included age about three ANC&#x27;s on but a general win it two times three this number three reading 12 different. We wanted everything by one out of three. No phone we have entirely rebuilt the most in Could you one of the three times? Table three. Thanks. Let&#x27;s see. It was even if I get included a Jew. Eva three experts see And to find out value, say here, you know after their own echo to five and everyone is doing some unit two plus C now for the same in CO. 203 and the and weeks again that untimely ripped UMA Zenkoji that you able three x plus three

Linh Vu · Answer

you noticed that if we do dear with the F Thanks the monetary thanks and we do the river doing it. Nico Gina three ju over three terms. Uh, a about three angst and better general winded you again. Temps three here and we can certify the tribute a tree. And again that you be about three x exactly cocina function. G X is only being a function f x. From here we can conclude that if thanks is the untie Dear Eva till Ah, but she angst.

Margaret Keymakh · Answer

she showed that this is equal went to be explicit. 13 slurred. And so just let&#x27;s just take me as I driven and make sure that this matches what question gives us. So did us. We&#x27;re gonna have to use a little bit of a substitution. So in this case, you is able to act. Um, you Oops. And that means that, do you? It&#x27;s just anything equal to Jack&#x27;s. Since the jury move past this one through, the 13 is a constant zero. So you d x on, then we can just go ahead and blood. So when we do that, you get integral of you swear? Yeah, urging you. And now we can use the universe. How rule of energy that I wanted to be. Excellent buy. So you swear it isn&#x27;t it? Well, you two the third number three plus c Now unplug the human, which is exposed routine Do that. We get at what&#x27;s 13. She&#x27;s very talented. Over three plus. And so, in fact, this is exactly the safe out of the tiger. So through this, we showed that there

Noah Duncan · Answer

Okay, So in this problem, we want to find an anti derivative for the function f of X equals X squared. To do that, we&#x27;re going to take indefinite integral of X squared DX because this is what it means Thio find, ah, the entire family of anti derivatives, and then we&#x27;ll just pick one from there. So to do this, normally we would take the anti derivative term. By term, I only have one term here with the X squared, so we&#x27;re just gonna use the power rule to figure that out. So the way that works is we&#x27;re gonna add one to the exponents, so two becomes three, and then we&#x27;re gonna divide by the new exponents. That&#x27;s the same thing, is multiplying by 1/3. And then there&#x27;s always ah, plus C that we add to the anti derivative. Because if you take the derivative of this term here, the 1/3 x cubed eyes going to become X squared, and the sea is going to become a zero when you take the derivative. So that&#x27;s why this would be an anti derivative of X squared because it would give it, Give it back to you. Um for this problem, we only need to pick one anti derivative. So let&#x27;s just set C equal to zero, for example and the anti derivative that we would have, um will be 1/3 excuse to see. Could say something like F of X equals 1/3 x cubed as your answer.

Noah Duncan · Answer

Okay, So in this problem, want to find an anti derivative of the function f of X equals X to the fourth power. And so to do this, we&#x27;re going to take the indefinite integral of X to the fourth DX. This will give us all of the different anti derivatives for F of X and a general form, and then we can pick one from there. So to do this, normally we go turn by term, only have one term here with the X to the fourth. So we&#x27;ll just do that one. And we do it using the power rule. So that means that we add one to the power, so become five instead of four. And then we divide that term by the same number, so it&#x27;ll be 1/5 x to the fifth. And then we do our plus C to make it the family of functions. The sea could be anything from zero to infinity or negative infinity. Um, whatever you want to be, any of those would be valid, because when we take the derivative of this function, this part becomes extra. The fourth and this part just become zero settle. We&#x27;ll be back to X to the fourth. No matter what, see you choose. So this is the family of anti derivatives. But for this problem, we only need to select one. So let&#x27;s just say, uh, one C equals zero. So in answer to this problem would just be x two x big fx.

Problem

Determine the value of a that makes $F(x)$ an ant…

Problem 5 Easy Difficulty

Determine the value of a that makes $F(x)$ an antiderivative of $f(x)$
$$f(x)=3 x^{2}, F(x)=a x^{3}$$

Answer

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

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Basic Technical Mathematics with Calculus