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

$ f(x) = 1 + 2\sin x + 3/\sqrt{x} $

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01:26

Fahad Paryani

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Derivatives

Differentiation

Volume

Campbell University

University of Michigan - Ann Arbor

Boston College

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're looking to take the anti derivative of the given function. So our function is cases F of X equals one Plus 2 Cynics. Okay. Mhm. Plus three over the square root of X is our function. Um And I would like to write three over the square root of act as three times X to the negative one half. That's gonna help us in the long run when we keep the anti derivative. Well we know that the anti derivative of this constant, we're just the X. Class. We know that the anti drone of cynics is a negative co signs will have negative to cosign X class when we add we'll have three times when we add one to the exponents here. That'll be one half. So three X to the one half divided by one half will mean multiplied by to also be a six X. The one half final answer.

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