Quick questions on Integration by partial fractions in HSC Mathematics Extension 2: decomposing rational functions over linear, repeated and irreducible quadratic factors and integrating

Q: What is too few terms for a repeated factor?

A factor (x - a)^2 needs both (A)/(x-a) and (B)/((x-a)^2). Using only one term loses a degree of freedom.

Q: What is a constant numerator over an irreducible quadratic?

An irreducible quadratic factor needs a linear numerator Bx + C, not just a constant.

2short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is too few terms for a repeated factor?

Show answer

A factor

(x - a)^2

needs both

\frac{A}{x-a}

and

\frac{B}{(x-a)^2}

. Using only one term loses a degree of freedom.

What is a constant numerator over an irreducible quadratic?

Show answer

An irreducible quadratic factor needs a linear numerator

Bx + C

, not just a constant.

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