Definite Integrals

Definite Integrals

What is it?

If F'=f, integral_a^b f(x)dx=F(b)-F(a); no +C remains.

In simple words

• If F'=f, integral_a^b f(x)dx=F(b)-F(a); no +C remains.
• Worked pattern: Integral0² 3x² dx=[x³]0²=8.
• Final check: domain, sign, notation, units, and reasonableness.

Important terms

Definite integrals: If F'=f, integral_a^b f(x)dx=F(b)-F(a); no +C remains.

What you should learn

• State the rule for definite integrals.
• Solve a definite integrals problem step by step.
• Check the result, restrictions, notation, and units.

Full school-level explanation

If F'=f, integral_a^b f(x)dx=F(b)-F(a); no +C remains.

CONCEPT AND RULE

If F'=f, integral_a^b f(x)dx=F(b)-F(a); no +C remains.

METHOD

For definite 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

Integral₀² 3x² dx=[x³]₀²=8.

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 definite integrals

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

• Definite integrals
• rule
• worked example
• worked example

How the ideas connect

Worked example: Integral0² 3x² dx=[x³]0²=8.

Deeper understanding

Go beyond memorising Definite Integrals. Connect the definition to reasons, relationships, exceptions, and exam wording.

How the ideas connect

Worked example: Integral0² 3x² dx=[x³]0²=8.

Common mistakes

Exam focus

Core Idea

Rule / Formula

Method

Worked Example

Exam focus

Quick revision

• Definite integrals
• rule
• worked example
• Definite integrals: If F'=f, integral_a^b f(x)dx=F(b)-F(a); no +C remains.
• CONCEPT AND RULE: If F'=f, integral_a^b f(x)dx=F(b)-F(a); no +C remains.
• METHOD: For definite integrals, identify the given information and required result. Select the matching defi

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 Definite Integrals: define clearly → explain the main parts → give one example → state one exam caution.