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Antidifferentiation of Polynomial Functions (VCE SSCE Mathematical Methods): Quizzes

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Antidifferentiation of Polynomial Functions

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What is antidifferentiation?

The reverse process of differentiation

If two functions have the same derivative, how do they differ?

They differ only by a constant

What is $\int x^5 \, dx$ equal to?

$\frac{x^6}{6} + c$

In the power rule for antidifferentiation, what two steps do you follow?

Increase power by one, divide by new power

What is $\int 1 \, dx$ equal to?

$x + c$

What is $\int 4x^3 \, dx$ equal to?

$x^4 + c$

When finding $\int (x^2 + x^3 + x) \, dx$ , how many constants $c$ are needed?

One constant at the end

What is $\int (2x^2 + 3x) \, dx$ equal to?

$\frac{2x^3}{3} + \frac{3x^2}{2} + c$

If $f'(x) = 6x^2$ and $f(0) = 5$ , what is $f(x)$ ?

$2x^3 + 5$

If $\frac{dy}{dx} = 2x$ and $y = 3$ when $x = 0$ , what is $c$ ?

$3$

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