Problem

Determine the value of a that makes $F(x)$ an ant…

Problem 11 Easy Difficulty

Determine the value of a that makes $F(x)$ an antiderivative of $f(x)$
$$f(x)=\frac{1}{x^{2}}, F(x)=\frac{a}{x}$$

Answer

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Calculus 1 / AB

Basic Technical Mathematics with Calculus

Chapter 25

Integration

Section 1

Antiderivatives

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Video Transcript

we want to find the Carson A. Such that capital F X equals a over X is an anti derivative of the function F X equals one over X squared. This question is challenging our understanding of anti differentiation as a precursor to integration as such. We need to understand how antivirus work. So remember that an anti derivative is the university roommate. For this reason we have to know derivative rules such as one through three are listed here for this fx equals one over X. Where we only need to use the power rule. Since for the revenues and states CVS extra equals a actually a minus one. The inverse must take the anti derivative of extra. A. Is one over a Actually a Plus one. So we must have for X. F X equals one of X squared anti derivative F one equals negative one times one over X or F one equals negative one over X. To solve for a. We have to set capital f equal to F one. Thus we obtain for our solution negative wanna react equals X. A equals negative one

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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