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Find $ f $.

$ f'(t) = 3^t - 3/t $, $ \quad f(1) = 2 $, $ \quad f(-1) = 1 $

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Video by Carson Merrill

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01:40

Wen Zheng

00:44

Amrita Bhasin

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Derivatives

Differentiation

Volume

Campbell University

Harvey Mudd College

Baylor University

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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for this problem here, what we have is that F prime of X is equal to 3 to the T minus three Over Act So three of the Act -3 over X. So when we look at this, when we take the anti derivative, so F of X. That's going to give us the natural log. That's the US. 3 to the T mm Through the X over the natural log of three -3 times the natural log of the absolute value of X. So that right there is going to be our final answer. But then we have plus C. So when we use the initial conditions and plug in our value one, we end up getting too. So as a result, we know that it'll be plus or minus your 0.7. It's not right. There is going to be our final answer for the anti derivative of F prime of X.

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