P1.5 - Integration

Indefinite integration as the reverse Students should know that a constant of integration is of differentiation. required.

Use indefinite integration as the reverse to connect the rule to the data and decision in the question.

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

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

Boundary: Indefinite integration as the reverse is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Integration of xn and related sums, (Excluding n = −1 and related sums, differences and differences and constant multiples. multiples).; For example, the ability to integrate expressions such as 1 x2 −3x −1 2 and (x + 2)2 is expected. x Given f ′(x) and a point on the curve, students should be able to find an equation of the curve in the form y = f(x).

Use integration of powers of x and related sums to connect the rule to the data and decision in the question.

This matters because integration of powers of x and related sums determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply integration of powers of x and related sums to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Integration of powers of x and related sums is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.