find-antiderivatives-of-the-given-functions-ft6-t312-3

Question

Find antiderivatives of the given functions.
$$f(t)=6 t^{3}+12$$

Tyler Moulton · Accepted Answer

we want to find the anti derivative of a function F of X is equal to six X cubed plus 12. To do so we need to have a solid understanding of anti differentiation which is a precursor integration and single variable count. So remember that the anti derivative is just the inverse derivative. That means we understand derivative rules. We can find an anti derivative for both six X cubed and 12. We only need to make use of rule one out of rules one through three are listed here. That is the power rule. Since the power rule states were derivatives. DDX actually A is a T A X to the a minus one. It holds that for the anti directive. Actually A we search for one over A plus one, actually a plus one. So taking anti derivative of fx we have capital F X equals six times 1/4 X to the fourth plus 12 X. On the second term for 12 we add a factor of expresses the constant. That&#x27;s we have final solution. Capital F X is three halfs X to the fourth plus 12 X.

Linh Vu · Answer

in this question, we need to find an indefinite integral off the T bird. Three for 60 square. Did they recall the power from the indefinite integral triple nd tree? You could get a table. And this one off, Empress, one plus constancy is in this formula. Now, for the first term, we will have a table for far for a second term. The six we stayed the same, they would have a table 3/3, plus a constancy. It was in a fight. And then we get Nico Judah. Thus Judy tree policy.

Amrita Bhasin · Answer

The first thing we know is that we can break up the integral so pulling out, too, because it&#x27;s a constant we have two Integral of Axe Jackson pulling out the sex because it&#x27;s a constant co sign. Axe DX The supplies to two x squared, divided by two with six sign x Plus e, which simplifies to simply X squared plus six sign x plus e Now, this point me no see is a constant. You know, the half of pious pi squared plus two. So given this weaken set pi squared plus two equals pi squared plus six sign pie plus C Giving us C equals pi squared plus two minus pi squared So pious cripples two mice Passport Just to cause the pie Sports cancel out So our final equation after vax equals X squared plus six sine x plus two

Linh Vu · Answer

in this question, we need to find an tiny river off the table three minus city square with ju honest day D d Derek OrNda You would have the power through Rebel and DT there. We get any coaching TVA and it&#x27;s one of the and this one. Plus the constancy is in this formula here. They can no do one by one. For the first time here we get in community now Dreamed us when it could have far off from minus here. Uh, r two will be the constant We came it outside times. Now about to bless one would be t about three on with three minus Doesn&#x27;t means them with table one. So we have one. This one will be t about. You are with you. Press a constancy in which me forget a table for far Ministry. Bela tree Almost six months stay. But you are what you plus a constant C

Bobby Barnes · Answer

we want to evaluate this definite Andrew here. Now they tell us in the chapter that we integrate one over you that should give us the natural log of the absolute value of you. Plus C. Let&#x27;s see if we can actually make orange Girl look like that. Well, maybe we then let our denominator be, Are you? If we do it, use up and taking the derivative of this with respect to tea and getting our different troll, we talked D u is able to three times. Well, the driven of a tangent is seeking squared. So it be seeking square T d t. And we&#x27;ll look at that. That&#x27;s exactly what we have here. So that&#x27;s going to become d&#x27;you over our denominator was you and we integrate this so there&#x27;s going to be the natural log of the absolute value of you, plus her constancy. Then we would just take you, plug it in so we&#x27;d get our definite Nicholas the natural log of the absolute value of six plus three Tanja T plus our constant C or our definite

Linh Vu · Answer

the question we need to find indefinitely into girl Off the tape, our trounce dick d recording the power ruled deeper and DT we could get a table And this one of amorous one trust comes to see Therefore we have an he included drowned don&#x27;t have Deba trembles when we&#x27;re being setting off a thing that&#x27;s a constant C.

Problem

Find antiderivatives of the given functions. $$f(…

Problem 15 Easy Difficulty

Find antiderivatives of the given functions.
$$f(t)=6 t^{3}+12$$

Answer

$F(t)=\frac{3}{2} t^{4}+12 t$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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$F(t)=\frac{3}{2} t^{4}+12 t$

Basic Technical Mathematics with Calculus

Catherine R.

Anna Marie V.

Heather Z.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Catherine R.

Anna Marie V.

Heather Z.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus