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

$ f(x) = x^{3.4} - 2x^{\sqrt{2-1}} $

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01:45

Fahad Paryani

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Derivatives

Differentiation

Volume

University of Michigan - Ann Arbor

Idaho State University

Boston College

Lectures

04:35

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.

06:14

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 we want to find the most general anti derivative have this function. The function is F of X equals Next to 3.4. Yeah. Plus minus two. X. Finance two. X to the square root of two. So now that we have this um we want this is actually dispirited too minus one, two minus one. So that's what we have as a result. So our F of X. The anti derivative. Yeah. Is going to be the anti directive each the individual terms. So X to the 3.4 we take used the power rule. That's going to give us X to the 4.4 over 4.4. And that's getting -2 times x. The power. So we're going to add one which is get rid of this negative one here. So if you need to the power of the square root of two Over the Square Root of two. And all we have to do is that our constancy. And as a result of this, if we take F prime of X and just choose a random constant C. Regardless of what the constant is. Our F prime of X. Craft is the same as the original F graph, so we've done this correctly.

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