P4.6 - Integration

Evaluation of volume of revolution. π ∫ y2 dx is required, but not π ∫ x2 dy.; Students should be able to find a volume of revolution, given parametric equations.

Use evaluation of volume of revolution to connect the rule to the data and decision in the question.

This matters because evaluation of volume of revolution determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply evaluation of volume of revolution to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Evaluation of volume of revolution is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Simple cases of integration by Students will be expected to use a substitution to find, e.g. substitution and integration by ∫ x x − 2 dx parts.; Understand these methods as the reverse processes of the chain The substitution will be given in more complicated and product rules respectively. integrals. ∫ The integral ln x dx is required.; More than one application of integration by parts may be required, for example, ∫ x2ex dx, ∫ ex sin x dx.

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

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

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

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

Simple cases of integration using Integration of rational expressions such as those arising partial fractions. 2 3 from partial fractions, e.g.,. 3x +5 (x −1)2 Note that the integration of other rational expressions, such x 2 as and is also required x2 +5 (2x −1)4 (see P3 section 5.2).

Use simple cases of integration to connect the rule to the data and decision in the question.

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

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

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

Analytical solution of simple first General and particular solutions will be required. order differential equations with separable variables.

Use analytical solution of simple first to connect the rule to the data and decision in the question.

This matters because analytical solution of simple first determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply analytical solution of simple first to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Analytical solution of simple first is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Use integration to find the area Students should be able to find the area under a curve given under a curve given its parametric its parametric equations.; Students will not be expected to equations. sketch a curve from its parametric equations.

Use use integration to find the area to connect the rule to the data and decision in the question.

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

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

Boundary: Use integration to find the area is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.