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Find the most general antiderivative of the function. (Check your answers by differentiation.)

$ f(x) = \dfrac{1}{5} - \dfrac{2}{x} $

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01:07

Fahad Paryani

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Derivatives

Differentiation

Volume

Oregon State University

Baylor University

University of Michigan - Ann Arbor

Lectures

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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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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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Find the most general anti…

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So for this problem, we want to produce the most general anti derivative of the function And the function that we're given is 1/5 -2 over X. So f of x. because 1 5th -2 over X. And we want to remember that one over X, the anti derivative of that is going to be the natural log of X. So what this is going to give us is 1/5 x minus two times the natural log of the absolute value of acts. All right. There is going to be our final answer, but we want to remember that there is going to be a constant classy. Um and we just know that X cannot equal zero. So it's this right here where X cannot equal zero is supposed to be our final function. If we took a crime of X and chose a different value of C, we see that this is the exact same graph given to us.

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