MathematicsChapter 3: Integration
Checking An Integral
Differentiate an indefinite answer, estimate sign and size, and verify limits for definite work.
Learning objectives
- State the rule for checking an integral.
- Solve a checking an integral problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Differentiate an indefinite answer, estimate sign and size, and verify limits for definite work.
Formula
dx=2x(x2+1)3.
Where / symbols
- Checking an integral
- Differentiate an indefinite answer, estimate sign and size, and verify limits for definite work.
CONCEPT AND RULE
Differentiate an indefinite answer, estimate sign and size, and verify limits for definite work.
METHOD
For checking an integral, 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
d[(x2+1)frac44]/dx=2x(x2+1)3.
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 checking an integral
- 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:
- d[(x2+1)frac44]/dx=2x(x2+1)3.
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
- Checking an integral
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Checking An Integral
Sticky Notes · Formula and Worked Revision
Core Idea
- Differentiate an indefinite answer, estimate sign and size, and verify limits for definite work.
Rule / Formula
- Differentiate an indefinite answer, estimate sign and size, and verify limits for definite work.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- d[(x2+1)frac44]/dx=2x(x2+1)3.
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
- Differentiate an indefinite answer, estimate sign and size, and verify limits for definite work.
- Worked pattern: d[(x2+1)frac44]/dx=2x(x2+1)3.
- Final check: domain, sign, notation, units, and reasonableness.
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