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## Homework Statement

I need to show that the area function for a parabola in the first quadrant is constant.

## Homework Equations

[tex] A(a) = \int^a_0 \frac{1}{a}-\frac{x^2}{a^3}\,dx [/tex]

## The Attempt at a Solution

Computing this integral gives an area of 2/3. Since the area will always be 2/3 and does not depend on the value of a, then the area function is constant. However, my question is about showing that the area function is constant using the Fundamental Theorem of Calculus.

Can I use the FTC, legitimately? Or is the hypothesis of the FTC not satisfied because of the division by a in the integrand?

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