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Determine the value of a that makes $F(x)$ an antiderivative of $f(x)$$$f(x)=10 x^{1 / 4}, F(x)=a x^{5 / 4}$$

Calculus 1 / AB

Chapter 25

Integration

Section 1

Antiderivatives

Integrals

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we want to find the constant A. Such the capital F X equals a. X. To the 5/4. As an anti derivative of the function of x equals 10 X to the 1/4. This question is challenging understanding of anti differentiation as a precursor integration. We need to make sure we understand this topic before proceeding so remember that the anti derivative is just the inverse derivative. So for this reason we need to understand D X. Or derivative rules, which is one through three listed here. For this particular problem, we need to use the power rule. Since the power rule states for derivatives, db X x A equals A. Actually a minus one. It must be by the inverse of the anti rated X. D. A is one over A actually a plus one. Using this rule. We therefore have at the anti derivative F of X is F one. It goes 10 times 4 50 extra 5/4 or eight times. Actually by force we saw for a by setting F one equal to capital F. In doing so we obtain our solution that is A. is equal to eight

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