P2.8 - Integration

Evaluation of definite integrals.

Use evaluation of definite integrals to connect the rule to the data and decision in the question.

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

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

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

Interpretation of the definite Students will be expected to be able to evaluate the area of integral as the area under a curve. a region bounded by a curve and given straight lines.; For example, find the finite area bounded by the curve y = 6x − x2 and the line y = 2x. ∫ x dy will not be required.; Students will be expected to be able to evaluate the area of a region bounded by two curves.

Use interpretation of the definite to connect the rule to the data and decision in the question.

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

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

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

Approximation of area under a For example, curve using the trapezium rule. use the trapezium rule to approximate ∫ (2x +1) dx using four strips.; Use of increasing number of trapezia to improve accuracy and an estimate of the error may be required.

Use trapezium rule for area approximation to connect the rule to the data and decision in the question.

This matters because trapezium rule for area approximation determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply trapezium rule for area approximation to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Trapezium rule for area approximation is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.