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Checking an Integral
Differentiate an indefinite answer, estimate sign and size, and verify limits for definite work.
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Checking an Integral
What is it?
Differentiate an indefinite answer, estimate sign and size, and verify limits for definite work.
In simple words
- 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.
Important terms
Checking an integral: Differentiate an indefinite answer, estimate sign and size, and verify limits for definite work.
What you should learn
- State the rule for checking an integral.
- Solve a checking an integral problem step by step.
- Check the result, restrictions, notation, and units.
Recommended for Class 12
Full school-level explanation
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
How it works
- 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.
Remember
- Checking an integral
- rule
- worked example
- worked example
How the ideas connect
Worked example: d[(x2+1)frac44]/dx=2x(x2+1)3.
Deeper understanding
Go beyond memorising Checking an Integral. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked example: d[(x2+1)frac44]/dx=2x(x2+1)3.
Common mistakes
Exam focus
Core Idea
Rule / Formula
Method
Worked Example
Exam focus
Quick revision
- Checking an integral
- rule
- worked example
- 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 de
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
For long answers on Checking an Integral: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Checking an integral
- rule
- worked example
- Checking an integral: Differentiate an indefinite answer, estimate sign and size, and verify limits for definite work.
Important formulas
- Checking an integral
- rule
- worked example
Common exam traps
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- A matching-looking formula is not valid until its conditions and domain have been checked.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- Mistake
A matching-looking formula is not valid until its conditions and domain have been checked.
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Checking an integral
rule
worked example
Checking an integral: Differentiate an indefinite answer, estimate sign and size, and verify limits for definite work.
Differentiate an indefinite answer, estimate sign and size, and verify limits for definite work.
- Definition
- Differentiate an indefinite answer, estimate sign and size, and verify limits for definite work.
- Critical warning
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all d
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Exam Practice
Define
Q1. Define Checking an Integral.
Explain
Q2. Explain: CONCEPT AND RULE.
Example
Q3. Give one clear example of Checking an Integral and say why it fits.
Mistake
Q4. State one common mistake students make about Checking an Integral.
Exam note
Q5. Write a short exam note on Checking an Integral: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.