Choose the correct quantity to fill in the blank:

Integral_______ dx = (ax2 - a2)4 + C.

to do this, we get the derivative of (ax^2 - a^2)^4 + c

assuming a is constant, the derivative is
4[(ax^2 - a^2)^3](2ax)

hope this helps~ :)

To determine the correct quantity to fill in the blank, let's analyze the given expression. The integral is written as ∫f(x) dx, where f(x) represents the integrand function and dx indicates that we are integrating with respect to x.

In this case, the integrand function is missing. However, we are provided with the result of the integration, which is (ax^2 - a^2)4 + C.

To find the original function, we need to differentiate (ax^2 - a^2)4 + C with respect to x, which will lead us back to the integrand function.

Differentiating (ax^2 - a^2)4 + C:

d/dx [(ax^2 - a^2)4 + C] = 4(ax^2 - a^2)3 * 2ax = 8a(ax^2 - a^2)x

If we compare this result to the general formula for the derivative of a function, we can determine the integrand function:

f(x) = 8a(ax^2 - a^2)x

Therefore, the correct quantity to fill in the blank is 8a(ax^2 - a^2)x:

∫[8a(ax^2 - a^2)x] dx = (ax^2 - a^2)4 + C