VCE Together Year 12 Mathematical Methods: Anti-Derivatives of Polynomial Functions

Mathematical Methods

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Anti-Derivatives of Polynomial Functions

Anti-derivatives of polynomial functions is part of the VCE Maths Methods topic Calculus and subtopic Applications of Differentiation.

In this post, we define anti-differentiation as the reverse of differentiation and use the notation \int f(x) dx for anti-derivatives or indefinite integrals. We also recognise that any two anti-derivatives of f(x) differ by a constant.

We also establish and use the formula \int x^{n} dx = \frac{1}{n+1} x^{n+1} + C for n \neq 1 .

Primitive Functions

To understand anti-differentiation, we must first understand the concept of the primitive. This will be explained in the following two videos. The first video will introduce the concept of primitive functions, and the second video will support this with examples.

Part 2

The Importance of the Constant

The following video will explain the importance of the constant term.

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