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Find the antiderivative F of f(t) sec? t, where F=1...

Question

Find the antiderivative F of f(t) sec? t, where F=1

Find the antiderivative F of f(t) sec? t, where F =1



Answers

Find an antiderivative. $$f(t)=\frac{t^{2}+1}{t}$$

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'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'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're just gonna use the power rule to figure that out. So the way that works is we're gonna add one to the exponents, so two becomes three, and then we're gonna divide by the new exponents. That's the same thing, is multiplying by 1/3. And then there'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'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'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.

Okay, so this problem won't find a kn anti derivative for the function F T equals five t And to do this, we're going Thio take E uh, indefinite. Integral of five T d t. Um And so this is just going to give us the family of anti derivatives, and we can just pick one from there for answer. So to do this, we can just pull out the five. The five of the constant, um, we're just gonna evaluate this. We normally just go turn by term, only one term here to evaluate. So just gonna pull out the five and then for the tea. We're going to, um, raised the exponents by one, so it's gonna become t squared, and then we're gonna divide by the exponents. So that's the same thing is multiplying by 1/2. So then simplifying this, we would get five halfs, five tons of half t squared. And this is, um, an anti derivative of, um five tee hee of five t here. All of the anti derivatives have this plus C term here. And that's because if you take the fewer to take the derivative of this term, this part would go back to five teeth and this part would become zero so you can plug in whenever you want for sea. Here. Uh, the answer that we're going to go with is just going to be this five halves.

In this question were given the function F x equal agenda X squared plus one. And we need to find the anti derivative Captain F X. Yeah, We use a formal on fund of power room here. You get a good expert and this one off endless one plus a constant C. Yeah. For the first time here, we get equal to the expo entry on with three for the one here. We don't need your hand up. Thanks. Here and now. We don't forget your brother Constant. See your finest police say we know that I have observed in court you five and it we would've zone here in ISO hand and yeah, nafta would only to see their far doesn't implies that we have that. And tiny river. There you go to the experiment tree on with drapers. This five

In this question, we are required to find the general anti derivative of FT is equal to 60. So we can write and a derivative of 50 years integral off 50 D. T. This will be equal, do in detail. 06 PDT. This integral can be read in us six taken outside integral. OTDT. So this will be equal to six multiplied with The square by two. Now these two cancels out 63 times, so we get three d square plus a constant of integration c. c. This will become the final answer.


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