Answer :
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the relationship between F and A is x
A(x) = ∫ f(x)dx = F(x) -F(0)
0
the relationship between F and A is x
A(x) = ∫ f(x)dx = F(x) -F(0)
0
The relationship between f and A is [tex]\boxed{A\left( x \right) = \int {f\left( x \right)dx} }[/tex] and the relationship between F and A is [tex]\boxed{F\left( x \right) = A\left( x \right) + C}.[/tex]
Further explanation:
Given:
F is an anti-derivative of fand A is an area function of f.
Explanation:
The relationship between f and A can be obtained as follows,
[tex]A\left( x \right) = \int {f\left( x \right)dx}[/tex]
If F is an anti-anti-derivative of the function f and A is the area function of f, then the relationship between A and F can be obtained as follows,
[tex]F\left( x \right) = A\left( x \right) + C[/tex]
Here, [tex]A\left( x \right)[/tex] the area in terms of x and C is the constant.
The relationship between f and A is [tex]\boxed{A\left( x \right) = \int {f\left( x \right)dx} }[/tex] and the relationship between F and A is [tex]\boxed{F\left( x \right) = A\left( x \right) + C}.[/tex]
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Derivatives
Keywords: Derivative, function, differentiate, minimum value, F, anti-derivative, f, area, A, function, relationship, relation, integral, differentiation.