P1.5.2 - Integration of powers of x and related sums

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.