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Question

Find antiderivatives of the given functions.
$$f(p)=4\left(p^{2}-1\right)^{3}(2 p)$$

Tyler Moulton · Accepted Answer

we want to find that the anti derivative of the function F of X is equal to four times x squared minus one few times two X. This question is testing our knowledge of anti differentiation as a precursor to integration as such. We need to be able to solve an anti derivative. Remember that an anti derivative is just an inverse derivative. Therefore, if we understand the rules for taking derivatives we can take you find the inverse rule for taking anti drill bits. This particular problem we need both. Rule one, the power rule and as I&#x27;ve highlighted, rule three, the chain rule, if you take the derivative of X squared minus one to some A by the chain rule, you&#x27;re always going to produce a factor of two X. Therefore if you take the anti derivative, it must be that the anti derivative of maternal experiments. One cube must absorb a factor of two X. So we must have the capital fx is four times one. Fourth experiments. One of the fourth by the power rule, times two X over two X absorbing the chain rule. This gives final solution for capital, F x x squared minus one the fourth power.

Grace Bajar · Answer

so we have to function. P A buck is equal to three seek in squared picks and we&#x27;re supposed to find the anti derivative of the function P of X. And this is just gonna be three 10 gin X plus C. And we know less because if we have g of X, is he going to three Hanjin X Plus E and then we take the dura. But above it, we get a three seeking squared six, which is our first function.

Amit Srivastava · Answer

we are given a function. B X is equal to three. Secret Square X willing to fund the anti derivative off this on very did it with taking the dedicated So that has finally ended a derivative sake you X is equal to integral of Seacon Square x three years Taking three outside in the grill of sick in school Rexes Panics plus c Not interested in deliberative of this u by d. X o three Then explicit si that&#x27;s it would be equal toe three. Indo Thai next deliver difference second square X plus zero This is a photo three second square x, and this is equal to the function given p x.

Amit Srivastava · Answer

we are given. Ah, function that is a 50 is it will do Seacon Square T. We need to find the anted elevated that satisfies the initial value that F at pie divided by four, is equal to one. Now the anti derivative function F T will be able to indignant off the function small if off t v, which is equal to integral off second squared a duty which will be equal toe Dante plus C. Now let&#x27;s put the condition of the initial value problem. We are given that if at by divided by four is equal to one which implies that then act by a divided by four plus C is equal to one. Now we know that Donald Spy divided by forest one Sovann policy is equal to one which gives us equal to zero. So therefore the final anted elevated function satisfying the given initial value problem will become equal toe Don be

Amit Srivastava · Answer

they are given a function that is small effort fly is equal to minus two. Divided by Vike You We need to find the entered elevated for the given function. So let capital f off. Why be the anti derivative function off? Small effort? Fight So in that case, what weaken right? Since we know that the dead innovative D upon divi off the function virus to the part off minus to plus C will become equal to minus two, why raise to the part off minus two minus fund ritual people to minus two violence to the part of my list. Three visual people to minus two, divided by y Cube, which is the acquired function. So therefore, we can say the capital effort by which is equal to wireless to the part of minus two policy is the anti dead, innovative function off the given function. If off what

Grace Bajar · Answer

in this problem were asked to give the anti derivative of exit api No. One. We&#x27;re taking the anti derivative. We know that we add one to the exponents every multiply it by the inverse of the exponents over Gonna have. So in our problem, we will have one over p plus one x to the P plus one. And this will go with any interred Europea.

Problem

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

Problem 31 Easy Difficulty

Find antiderivatives of the given functions.
$$f(p)=4\left(p^{2}-1\right)^{3}(2 p)$$

Answer

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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Precalculus Review - Intro

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

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