MathematicsChapter 3: Integration
Antiderivatives and Constants
An antiderivative F satisfies F'=f; indefinite integrals require +C because constants differentiate to zero.
Learning objectives
- State the rule for antiderivatives and constants.
- Solve a antiderivatives and constants problem step by step.
- Check the result, restrictions, notation, and units.
Definition
An antiderivative F satisfies F'=f; indefinite integrals require +C because constants differentiate to zero.
Where / symbols
- Antiderivatives and constants
- An antiderivative F satisfies F'=f; indefinite integrals require +C because constants differentiate to zero.
CONCEPT AND RULE
An antiderivative F satisfies F'=f; indefinite integrals require +C because constants differentiate to zero.
METHOD
For antiderivatives and constants, 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 of 6x dx is 3x^2+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 antiderivatives and constants
- 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 of 6x dx is 3x^2+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
- Antiderivatives and constants
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Antiderivatives and Constants
Sticky Notes · Formula and Worked Revision
Core Idea
- An antiderivative F satisfies F'=f; indefinite integrals require +C because constants differentiate to zero.
Rule / Formula
- An antiderivative F satisfies F'=f; indefinite integrals require +C because constants differentiate to zero.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- Integral of 6x dx is 3x^2+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
- An antiderivative F satisfies F'=f; indefinite integrals require +C because constants differentiate to zero.
- Worked pattern: Integral of 6x dx is 3x^2+C.
- Final check: domain, sign, notation, units, and reasonableness.
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