MathematicsChapter 3: Integration
Basic Trigonometric Integrals
Recognize standard derivative pairs and keep signs accurate.
Learning objectives
- State the rule for basic trigonometric integrals.
- Solve a basic trigonometric integrals problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Recognize standard derivative pairs and keep signs accurate.
Mathematical form
dx=sin x+C
dx=-cos x+C.
Where / symbols
- Basic trigonometric integrals
- Recognize standard derivative pairs and keep signs accurate.
CONCEPT AND RULE
Recognize standard derivative pairs and keep signs accurate.
METHOD
For basic trigonometric integrals, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.
WORKED EXAMPLE
Integral cos x dx=sin x+C; integral sin x dx=-cos x+C.
COMMON MISTAKE
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
How to solve basic trigonometric integrals
- Identify the mathematical objects, givens, restrictions, and required result.
- Choose and write the relevant definition, theorem, or formula.
- Substitute with brackets and carry out one justified step per line.
- Simplify, state the final answer clearly, and verify it in the original setting.
Worked example
- Worked example:
- Integral cos x dx=sin x+C; integral sin x dx=-cos x+C.
In simple words
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Key points
- Basic trigonometric integrals
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Basic Trigonometric Integrals
Sticky Notes · Formula and Worked Revision
Core Idea
- Recognize standard derivative pairs and keep signs accurate.
Rule / Formula
- Recognize standard derivative pairs and keep signs accurate.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- Integral cos x dx=sin x+C; integral sin x dx=-cos x+C.
Common Error
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
FBISE Exam Tip
- Show the formula, substitutions, algebra, restrictions, and final answer; method marks need visible reasoning.
60-second revision
- Recognize standard derivative pairs and keep signs accurate.
- Worked pattern: Integral cos x dx=sin x+C; integral sin x dx=-cos x+C.
- Final check: domain, sign, notation, units, and reasonableness.
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