Integration by Substitution

Integration by substitution is a core technique in the Further integration topic of NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-04). This subtopic changes the variable of integration to turn a hard integrand into a familiar one, for both indefinite and definite integrals, whether or not the substitution is given.

Students and teachers will cover choosing an effective substitution, handling odd powers of sine and cosine and powers of \(\tan x\) and \(\sec x\), and changing the limits of a definite integral — one of the most widely used integration methods in the HSC Extension 2 course.