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The graph of the velocity function of a particle …

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Problem 53 Medium Difficulty

The graph of a function is shown in the figure. Make a rough sketch of an antiderivative $ F $, given that $ F(0) = 1 $.


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03:24

WZ

Wen Zheng

00:48

Amrita Bhasin

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Related Topics

Derivatives

Differentiation

Volume

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Volume - Intro

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

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06:14

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Video Transcript

So given the graph of the function the picture, we want to give a rough estimate um for the sketch of the anti derivative F. And we know that F of zero is going to be equal to one. So the reason why we have those initial conditions and why they're extremely important is because we know that when we take F prime of X. A. So let's say F was equal to some value, you know, C. X plus the right. Well, we know that when we take F. Crime that that the value is going to go away. So when we take the integral of the derivative, we're going to get F back but we need to compensate for that. See that we might have lost. So as a result of that, we use the initial condition, the anti derivative that we're going to end up getting at least it's similar to that. It's going to be F equals the natural log of acts. For the negative natural log of acts plus X. Natural life of two minus, and that's where the initial condition comes in minus the natural log of two. So that's right here, it's going to be the final graphical representation that we see.

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Related Topics

Derivatives

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Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Catherine Ross

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Anna Marie Vagnozzi

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Samuel Hannah

University of Nottingham

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Lectures

Video Thumbnail

04:35

Volume - Intro

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

Video Thumbnail

06:14

Review

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

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