Principle of Calculus

Curriculum details

Strand

Calculus (Strand 3)

Sub-strand

Principle of Calculus (3.1)

Content standard

3.3.1.CS.1 - Demonstrate conceptual understanding of the rules and techniques of integration to select and apply them. appropriately to a function. 3.3.1.LO.1 Identify and apply the integration rules to evaluate integrals.

Indicator

3.3.1.LI.3 - Identify and apply appropriate techniques of integration to solve transcendental functions.

Suggested placement

Semester 2, Week 4 (Week 24 of the year)

Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.

Source document note

The official curriculum document has a fault in this entry, so the curriculum text above is transcribed exactly as printed:

• exemplars - p.512: adjacent duplicated CambriaMath characters were collapsed, but this PDF also maps some equation glyphs to the wrong letter or operator; verify every mathematical expression in this row against the rendered page
• exemplars - p.513: a stacked fraction, matrix, vector or other two-dimensional construct is flattened by the text layer; all visible parts require comparison with the rendered page

Curriculum reference

NaCCA curriculum document, p. 512

Exemplars (from the NaCCA curriculum)

Talk for Learning, Think-pair-share, Experiential Learning and Group Work/Collaborative Learning.
Activity 1: Integration of exponential and natural logarithm functions. Learners in their mixed-ability groups distinguish among techniques of integration of exponential and natural logarithm functions.
- ∫ 𝑒 l0 𝑑, 𝑘 𝑎 𝑐 ≠ 0 ! ∫ 𝑒 l0 𝑑 = l 𝑒 l0 + 𝐶, 𝑘 ≠ 0
!
- ∫ 0 𝑑 =𝑙 𝑙 |𝑥| + 𝐶, 𝑥 ≠ 0 J 1 (0)
- ∫ J(0) 𝑑 =𝑙 𝑙 |𝑔(𝑥| + 𝐶, 𝑥 ≠ 0
∫ 𝑒 W(0) 𝑑 𝑘 𝑎 𝑐 ≠ 0
- ∫ 𝑒 W(0) 𝑑 = W-(0) 𝑒 W(0) + 𝐶, 𝑘 ≠ 0 !
Example 1: Find the antiderivative of the following; !
- ∫ 0$1 𝑑 /
- ∫ /0$1 𝑑
- ) ∫ 0$1 𝑑 0
- ∫ (0 ! $/) 𝑑
D] (0)
- ∫ 𝑑 0 0 !
- ∫ 𝑥𝑒 𝑑
Activity 2: Evaluation of exponential function Learners in small groups solve problems on techniques of integration and present to the class.
- Compute ∫ i𝑥 *" + 7𝑒 .0 + 0 j 𝑑 ,
Solution: , , ∫ i𝑥 *" + 7𝑒 .0 + 0 j 𝑑 = ∫ 𝑥 *" 𝑑 + ∫ 7𝑒 .0 𝑑 + ∫ 0 𝑑
= ∫ 𝑥 *" 𝑑 + 7 ∫ 𝑒 .0 𝑑 + 4 ∫ 𝑑 𝑥 ! , = − ) 𝑥 *) + . 𝑒 .0 + 4 𝑙 𝑙 |𝑥| + 𝐶 ! 7
Teaching and Learning Resources:
- Reading resource colour pens
- Notebook
- Graph sheets
- Mathematical sets,
- Technological tools.
- Curriculum
- Card boards
Assessment (3.3.1.AS.3). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding.