P3.5.2 - Integration by recognition

Integration by recognition of For example, to include integration of tan x, sec2 2x. known derivatives to include Students are expected to be able to use trigonometric integrals of the form identities to integrate, for example, sin2 x, tan2 x, cos2 3x. ∫ f′(x) dx = ln (f(x)) + c and f(x) ∫ f′(x)[f(x)]n dx = [ f(x) ]n+1 + c n +1.

Use integration by recognition to connect the rule to the data and decision in the question.

This matters because integration by recognition determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply integration by recognition to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Integration by recognition is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.