💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Watch this step-by-step video, matched to your homework problem.

Try Numerade Free for 30 Days

Like

Report

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

Calculus 1 / AB

Chapter 25

Integration

Section 1

Antiderivatives

Integrals

Oregon State University

Idaho State University

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

00:42

Find all the antiderivativ…

00:46

Finding antiderivatives Fi…

01:03

Particular antiderivatives…

01:05

00:32

Give the antiderivatives o…

00:59

01:13

01:04

00:53

Find an antiderivative.

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'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'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.

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

Find all the antiderivatives of the following functions. Check your work by …

Finding antiderivatives Find all the antiderivatives of the following functi…

Particular antiderivatives For the following functions $f,$ find the antider…

Give the antiderivatives of $x^{p}$. For what values of $p$ does your answer…

Give the antiderivatives of $x^{p} .$ For what values of $p$ does your answe…

Find an antiderivative.$$p(t)=t^{3}-\frac{t^{2}}{2}-t$$

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.