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Determine the value of a that makes F(x) an antiderivative of f(x). f(x) = 9x^2, F(x) = ax^3

Question:

Determine the value of a that makes F(x) an antiderivative of f(x).

{eq}f(x) = 9x^2, F(x) = ax^3 {/eq}

Antiderivative:

If the derivative of function {eq}f {/eq} is said to be {eq}g {/eq} then the integral or antiderivative of {eq}g {/eq} is said to be {eq}f {/eq} or in other words we can say that it is reverse process of differentiation.

Answer and Explanation:


As we know that If the derivative of function {eq}f {/eq} is said to be {eq}g {/eq} then the integral or antiderivative of {eq}g {/eq} is said to be {eq}f {/eq} , hence :-

{eq}F'(x) = f(x)\Rightarrow 3ax^2 = 9x^2 \Rightarrow a = 3 {/eq} .


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